Permenter, Frank A geodesic interior-point method for linear optimization over symmetric cones. (English) Zbl 1519.90158 SIAM J. Optim. 33, No. 2, 1006-1034 (2023). MSC: 90C22 90C25 90C05 90C20 90C51 49M15 65K05 PDFBibTeX XMLCite \textit{F. Permenter}, SIAM J. Optim. 33, No. 2, 1006--1034 (2023; Zbl 1519.90158) Full Text: DOI arXiv
Tsuchiya, Takashi; Lourenço, Bruno F.; Muramatsu, Masakazu; Okuno, Takayuki A limiting analysis on regularization of singular SDP and its implication to infeasible interior-point algorithms. (English) Zbl 1519.90159 Math. Program. 200, No. 1 (A), 531-568 (2023). MSC: 90C22 90C25 90C51 90C31 65K05 PDFBibTeX XMLCite \textit{T. Tsuchiya} et al., Math. Program. 200, No. 1 (A), 531--568 (2023; Zbl 1519.90159) Full Text: DOI arXiv
Padovani, Cristina; Porcelli, Margherita A semidefinite programming approach for the projection onto the cone of negative semidefinite symmetric tensors with applications to solid mechanics. (English) Zbl 1502.90119 Calcolo 59, No. 4, Paper No. 33, 31 p. (2022). MSC: 90C22 74E10 90C51 74B20 PDFBibTeX XMLCite \textit{C. Padovani} and \textit{M. Porcelli}, Calcolo 59, No. 4, Paper No. 33, 31 p. (2022; Zbl 1502.90119) Full Text: DOI arXiv
Hespanha, João P. Tenscalc: a toolbox to generate fast code to solve nonlinear constrained minimizations and compute Nash equilibria. (English) Zbl 1496.90004 Math. Program. Comput. 14, No. 3, 451-496 (2022). MSC: 90-04 49-04 65K05 90C30 PDFBibTeX XMLCite \textit{J. P. Hespanha}, Math. Program. Comput. 14, No. 3, 451--496 (2022; Zbl 1496.90004) Full Text: DOI
Karimi, Mehdi; Tunçel, Levent Status determination by interior-point methods for convex optimization problems in domain-driven form. (English) Zbl 1494.90079 Math. Program. 194, No. 1-2 (A), 937-974 (2022). MSC: 90C25 90C51 49N15 65Y20 PDFBibTeX XMLCite \textit{M. Karimi} and \textit{L. Tunçel}, Math. Program. 194, No. 1--2 (A), 937--974 (2022; Zbl 1494.90079) Full Text: DOI arXiv
Faybusovich, Leonid; Zhou, Cunlu Long-step path-following algorithm for quantum information theory: some numerical aspects and applications. (English) Zbl 1487.90517 Numer. Algebra Control Optim. 12, No. 2, 445-467 (2022). MSC: 90C22 90C30 90C51 81-08 90C25 90C90 PDFBibTeX XMLCite \textit{L. Faybusovich} and \textit{C. Zhou}, Numer. Algebra Control Optim. 12, No. 2, 445--467 (2022; Zbl 1487.90517) Full Text: DOI arXiv
Kheirfam, Behrouz; Osmanpour, Naser A new wide-neighborhood predictor-corrector interior-point method for semidefinite optimization. (English) Zbl 1486.65060 J. Appl. Math. Comput. 68, No. 2, 1365-1385 (2022). MSC: 65K05 90C22 90C51 PDFBibTeX XMLCite \textit{B. Kheirfam} and \textit{N. Osmanpour}, J. Appl. Math. Comput. 68, No. 2, 1365--1385 (2022; Zbl 1486.65060) Full Text: DOI
Badenbroek, Riley; de Klerk, Etienne Complexity analysis of a sampling-based interior point method for convex optimization. (English) Zbl 1492.90120 Math. Oper. Res. 47, No. 1, 779-811 (2022). MSC: 90C25 90C51 PDFBibTeX XMLCite \textit{R. Badenbroek} and \textit{E. de Klerk}, Math. Oper. Res. 47, No. 1, 779--811 (2022; Zbl 1492.90120) Full Text: DOI arXiv
Kheirfam, Behrouz; Osmanpour, Naser; Keyanpour, Mohammad An arc-search infeasible interior-point method for semidefinite optimization with the negative infinity neighborhood. (English) Zbl 1476.90233 Numer. Algorithms 88, No. 1, 143-163 (2021). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{B. Kheirfam} et al., Numer. Algorithms 88, No. 1, 143--163 (2021; Zbl 1476.90233) Full Text: DOI
Chen, Zhongzhu; Fampa, Marcia; Lambert, Amélie; Lee, Jon Mixing convex-optimization bounds for maximum-entropy sampling. (English) Zbl 1473.90136 Math. Program. 188, No. 2(B), 539-568 (2021). MSC: 90C27 90C25 90C51 62K99 62H11 PDFBibTeX XMLCite \textit{Z. Chen} et al., Math. Program. 188, No. 2 (B), 539--568 (2021; Zbl 1473.90136) Full Text: DOI arXiv
Lin, Tianyi; Ma, Shiqian; Ye, Yinyu; Zhang, Shuzhong An ADMM-based interior-point method for large-scale linear programming. (English) Zbl 1470.90048 Optim. Methods Softw. 36, No. 2-3, 389-424 (2021). MSC: 90C05 90C06 90C51 PDFBibTeX XMLCite \textit{T. Lin} et al., Optim. Methods Softw. 36, No. 2--3, 389--424 (2021; Zbl 1470.90048) Full Text: DOI arXiv
Henrion, Didier; Naldi, Simone; Safey El Din, Mohab Exact algorithms for semidefinite programs with degenerate feasible set. (English) Zbl 1460.90128 J. Symb. Comput. 104, 942-959 (2021). MSC: 90C22 68W30 90C51 90C05 90C60 13P15 14P10 PDFBibTeX XMLCite \textit{D. Henrion} et al., J. Symb. Comput. 104, 942--959 (2021; Zbl 1460.90128) Full Text: DOI arXiv
Liu, Deyi; Tran-Dinh, Quoc An inexact interior-point Lagrangian decomposition algorithm with inexact oracles. (English) Zbl 1445.90082 J. Optim. Theory Appl. 185, No. 3, 903-926 (2020). MSC: 90C25 90-08 PDFBibTeX XMLCite \textit{D. Liu} and \textit{Q. Tran-Dinh}, J. Optim. Theory Appl. 185, No. 3, 903--926 (2020; Zbl 1445.90082) Full Text: DOI arXiv
Qian, Xun; Liao, Li-Zhi; Sun, Jie A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming. (English) Zbl 1435.90103 Math. Program. 179, No. 1-2 (A), 1-19 (2020). MSC: 90C22 90C51 90C25 37C75 37N40 PDFBibTeX XMLCite \textit{X. Qian} et al., Math. Program. 179, No. 1--2 (A), 1--19 (2020; Zbl 1435.90103) Full Text: DOI
Mohammad-Nezhad, Ali; Terlaky, Tamás Parametric analysis of semidefinite optimization. (English) Zbl 1434.90218 Optimization 69, No. 1, 187-216 (2020). MSC: 90C51 90C22 90C25 90C31 PDFBibTeX XMLCite \textit{A. Mohammad-Nezhad} and \textit{T. Terlaky}, Optimization 69, No. 1, 187--216 (2020; Zbl 1434.90218) Full Text: DOI arXiv
Sim, Chee-Khian Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: polynomial complexity and local convergence. (English) Zbl 1433.90172 Comput. Optim. Appl. 74, No. 2, 583-621 (2019). MSC: 90C33 90C51 PDFBibTeX XMLCite \textit{C.-K. Sim}, Comput. Optim. Appl. 74, No. 2, 583--621 (2019; Zbl 1433.90172) Full Text: DOI
Canelas, Alfredo; Carrasco, Miguel; López, Julio A feasible direction algorithm for nonlinear second-order cone programs. (English) Zbl 1431.90146 Optim. Methods Softw. 34, No. 6, 1322-1341 (2019). MSC: 90C30 49M15 90C51 PDFBibTeX XMLCite \textit{A. Canelas} et al., Optim. Methods Softw. 34, No. 6, 1322--1341 (2019; Zbl 1431.90146) Full Text: DOI
Bellavia, Stefania; Gondzio, Jacek; Porcelli, Margherita An inexact dual logarithmic barrier method for solving sparse semidefinite programs. (English) Zbl 1431.90108 Math. Program. 178, No. 1-2 (A), 109-143 (2019). MSC: 90C22 90C51 65F10 65F50 PDFBibTeX XMLCite \textit{S. Bellavia} et al., Math. Program. 178, No. 1--2 (A), 109--143 (2019; Zbl 1431.90108) Full Text: DOI Link
Cui, Yiran; Morikuni, Keiichi; Tsuchiya, Takashi; Hayami, Ken Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning. (English) Zbl 1427.90289 Comput. Optim. Appl. 74, No. 1, 143-176 (2019). MSC: 90C51 90C05 PDFBibTeX XMLCite \textit{Y. Cui} et al., Comput. Optim. Appl. 74, No. 1, 143--176 (2019; Zbl 1427.90289) Full Text: DOI arXiv
Faybusovich, Leonid; Zhou, Cunlu Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions. (English) Zbl 1420.90044 Comput. Optim. Appl. 72, No. 3, 769-795 (2019). MSC: 90C25 90C51 PDFBibTeX XMLCite \textit{L. Faybusovich} and \textit{C. Zhou}, Comput. Optim. Appl. 72, No. 3, 769--795 (2019; Zbl 1420.90044) Full Text: DOI
Laiu, M. Paul; Tits, André L. A constraint-reduced MPC algorithm for convex quadratic programming, with a modified active set identification scheme. (English) Zbl 1420.90042 Comput. Optim. Appl. 72, No. 3, 727-768 (2019). MSC: 90C20 90C25 90C51 PDFBibTeX XMLCite \textit{M. P. Laiu} and \textit{A. L. Tits}, Comput. Optim. Appl. 72, No. 3, 727--768 (2019; Zbl 1420.90042) Full Text: DOI arXiv
Alzalg, Baha A primal-dual interior-point method based on various selections of displacement step for symmetric optimization. (English) Zbl 1414.90322 Comput. Optim. Appl. 72, No. 2, 363-390 (2019). MSC: 90C30 90C46 90C51 17A15 PDFBibTeX XMLCite \textit{B. Alzalg}, Comput. Optim. Appl. 72, No. 2, 363--390 (2019; Zbl 1414.90322) Full Text: DOI
Campos, Juan S.; Misener, Ruth; Parpas, Panos A multilevel analysis of the Lasserre hierarchy. (English) Zbl 1430.90456 Eur. J. Oper. Res. 277, No. 1, 32-41 (2019). MSC: 90C22 90C26 90C20 PDFBibTeX XMLCite \textit{J. S. Campos} et al., Eur. J. Oper. Res. 277, No. 1, 32--41 (2019; Zbl 1430.90456) Full Text: DOI
Papp, Dávid; Yildiz, Sercan Sum-of-squares optimization without semidefinite programming. (English) Zbl 1412.90114 SIAM J. Optim. 29, No. 1, 822-851 (2019). MSC: 90C25 90C51 65D05 90C22 PDFBibTeX XMLCite \textit{D. Papp} and \textit{S. Yildiz}, SIAM J. Optim. 29, No. 1, 822--851 (2019; Zbl 1412.90114) Full Text: DOI arXiv
Tran-Dinh, Quoc; Kyrillidis, Anastasios; Cevher, Volkan A single-phase, proximal path-following framework. (English) Zbl 1440.90025 Math. Oper. Res. 43, No. 4, 1326-1347 (2018). MSC: 90C06 90C25 90-08 PDFBibTeX XMLCite \textit{Q. Tran-Dinh} et al., Math. Oper. Res. 43, No. 4, 1326--1347 (2018; Zbl 1440.90025) Full Text: DOI arXiv Link
Rigó, Petra Renáta; Darvay, Zsolt Infeasible interior-point method for symmetric optimization using a positive-asymptotic barrier. (English) Zbl 1409.90226 Comput. Optim. Appl. 71, No. 2, 483-508 (2018). MSC: 90C51 90C30 PDFBibTeX XMLCite \textit{P. R. Rigó} and \textit{Z. Darvay}, Comput. Optim. Appl. 71, No. 2, 483--508 (2018; Zbl 1409.90226) Full Text: DOI
Halická, Margaréta; Trnovská, Mária The Russell measure model: computational aspects, duality, and profit efficiency. (English) Zbl 1403.90509 Eur. J. Oper. Res. 268, No. 1, 386-397 (2018). MSC: 90C08 90C22 PDFBibTeX XMLCite \textit{M. Halická} and \textit{M. Trnovská}, Eur. J. Oper. Res. 268, No. 1, 386--397 (2018; Zbl 1403.90509) Full Text: DOI
Jarre, Florian; Lieder, Felix The solution of Euclidean norm trust region SQP subproblems via second-order cone programs: an overview and elementary introduction. (English) Zbl 1398.90206 Optim. Methods Softw. 33, No. 1, 70-91 (2018). MSC: 90C55 90C51 PDFBibTeX XMLCite \textit{F. Jarre} and \textit{F. Lieder}, Optim. Methods Softw. 33, No. 1, 70--91 (2018; Zbl 1398.90206) Full Text: DOI
Campos, Juan S.; Parpas, Panos A multigrid approach to SDP relaxations of sparse polynomial optimization problems. (English) Zbl 1398.90118 SIAM J. Optim. 28, No. 1, 1-29 (2018). MSC: 90C22 90C26 35G30 65H10 65N06 65N22 65N55 90C51 90C59 PDFBibTeX XMLCite \textit{J. S. Campos} and \textit{P. Parpas}, SIAM J. Optim. 28, No. 1, 1--29 (2018; Zbl 1398.90118) Full Text: DOI
Golany, B.; Goldberg, N.; Rothblum, U. G. A two-resource allocation algorithm with an application to large-scale zero-sum defensive games. (English) Zbl 1394.91248 Comput. Oper. Res. 78, 218-229 (2017). MSC: 91B32 91A05 65K05 90C06 90C51 PDFBibTeX XMLCite \textit{B. Golany} et al., Comput. Oper. Res. 78, 218--229 (2017; Zbl 1394.91248) Full Text: DOI
Permenter, Frank; Friberg, Henrik A.; Andersen, Erling D. Solving conic optimization problems via self-dual embedding and facial reduction: A unified approach. (English) Zbl 1368.90123 SIAM J. Optim. 27, No. 3, 1257-1282 (2017). MSC: 90C22 90C25 90C46 90C51 PDFBibTeX XMLCite \textit{F. Permenter} et al., SIAM J. Optim. 27, No. 3, 1257--1282 (2017; Zbl 1368.90123) Full Text: DOI
Mohammad-Nezhad, Ali; Terlaky, Tamás A polynomial primal-dual affine scaling algorithm for symmetric conic optimization. (English) Zbl 1360.90291 Comput. Optim. Appl. 66, No. 3, 577-600 (2017). MSC: 90C51 90C25 PDFBibTeX XMLCite \textit{A. Mohammad-Nezhad} and \textit{T. Terlaky}, Comput. Optim. Appl. 66, No. 3, 577--600 (2017; Zbl 1360.90291) Full Text: DOI
Wang, Timothy; Jobredeaux, Romain; Pantel, Marc; Garoche, Pierre-Loic; Feron, Eric; Henrion, Didier Credible autocoding of convex optimization algorithms. (English) Zbl 1364.90247 Optim. Eng. 17, No. 4, 781-812 (2016). MSC: 90C22 90C51 68N30 90C25 PDFBibTeX XMLCite \textit{T. Wang} et al., Optim. Eng. 17, No. 4, 781--812 (2016; Zbl 1364.90247) Full Text: DOI arXiv
Nayak, Rupaj Kumar; Desai, Jitamitra A modified homogeneous potential reduction algorithm for solving the monotone semidefinite linear complementarity problem. (English) Zbl 1380.90213 Optim. Lett. 10, No. 7, 1417-1448 (2016). MSC: 90C22 90C33 90C51 PDFBibTeX XMLCite \textit{R. K. Nayak} and \textit{J. Desai}, Optim. Lett. 10, No. 7, 1417--1448 (2016; Zbl 1380.90213) Full Text: DOI
Park, Sungwoo A constraint-reduced algorithm for semidefinite optimization problems with superlinear convergence. (English) Zbl 1344.90047 J. Optim. Theory Appl. 170, No. 2, 512-527 (2016). MSC: 90C22 65K05 90C51 PDFBibTeX XMLCite \textit{S. Park}, J. Optim. Theory Appl. 170, No. 2, 512--527 (2016; Zbl 1344.90047) Full Text: DOI
Valkonen, Tuomo A method for weighted projections to the positive definite cone. (English) Zbl 1327.90182 Optimization 64, No. 10, 2253-2275 (2015). MSC: 90C22 90C51 92C55 PDFBibTeX XMLCite \textit{T. Valkonen}, Optimization 64, No. 10, 2253--2275 (2015; Zbl 1327.90182) Full Text: DOI
Park, Sungwoo; O’Leary, Dianne P. A polynomial time constraint-reduced algorithm for semidefinite optimization problems. (English) Zbl 1329.90104 J. Optim. Theory Appl. 166, No. 2, 558-571 (2015). MSC: 90C22 65K05 90C51 PDFBibTeX XMLCite \textit{S. Park} and \textit{D. P. O'Leary}, J. Optim. Theory Appl. 166, No. 2, 558--571 (2015; Zbl 1329.90104) Full Text: DOI
Wang, G. Q.; Bai, Y. Q.; Gao, X. Y.; Wang, D. Z. Improved complexity analysis of full Nesterov-Todd step interior-point methods for semidefinite optimization. (English) Zbl 1322.90061 J. Optim. Theory Appl. 165, No. 1, 242-262 (2015). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{G. Q. Wang} et al., J. Optim. Theory Appl. 165, No. 1, 242--262 (2015; Zbl 1322.90061) Full Text: DOI
Harris, Matthew W.; Açıkmeşe, Behçet Lossless convexification of non-convex optimal control problems for state constrained linear systems. (English) Zbl 1297.49045 Automatica 50, No. 9, 2304-2311 (2014). MSC: 49M20 90C51 90C25 PDFBibTeX XMLCite \textit{M. W. Harris} and \textit{B. Açıkmeşe}, Automatica 50, No. 9, 2304--2311 (2014; Zbl 1297.49045) Full Text: DOI
Lipp, Thomas; Boyd, Stephen Minimum-time speed optimisation over a fixed path. (English) Zbl 1292.49035 Int. J. Control 87, No. 6, 1297-1311 (2014). MSC: 49M30 90C25 90C51 PDFBibTeX XMLCite \textit{T. Lipp} and \textit{S. Boyd}, Int. J. Control 87, No. 6, 1297--1311 (2014; Zbl 1292.49035) Full Text: DOI
Simon, J.-W.; Kreimeier, M.; Weichert, D. A selective strategy for shakedown analysis of engineering structures. (English) Zbl 1352.74231 Int. J. Numer. Methods Eng. 94, No. 11, 985-1014 (2013). MSC: 74P10 90C51 90C90 PDFBibTeX XMLCite \textit{J. W. Simon} et al., Int. J. Numer. Methods Eng. 94, No. 11, 985--1014 (2013; Zbl 1352.74231) Full Text: DOI
Lu, Zhaosong; Pong, Ting Kei Computing optimal experimental designs via interior point method. (English) Zbl 1425.62096 SIAM J. Matrix Anal. Appl. 34, No. 4, 1556-1580 (2013). MSC: 62K05 90C06 90C25 90C51 PDFBibTeX XMLCite \textit{Z. Lu} and \textit{T. K. Pong}, SIAM J. Matrix Anal. Appl. 34, No. 4, 1556--1580 (2013; Zbl 1425.62096) Full Text: DOI arXiv
Engau, Alexander; Anjos, Miguel F.; Bomze, Immanuel Constraint selection in a build-up interior-point cutting-plane method for solving relaxations of the stable-set problem. (English) Zbl 1272.90045 Math. Methods Oper. Res. 78, No. 1, 35-59 (2013). MSC: 90C22 90C51 90C09 90C20 90C27 90C35 90C90 PDFBibTeX XMLCite \textit{A. Engau} et al., Math. Methods Oper. Res. 78, No. 1, 35--59 (2013; Zbl 1272.90045) Full Text: DOI
Han, Le; Bi, Shujun; Pan, Shaohua Nonsingularity of FB system and constraint nondegeneracy in semidefinite programming. (English) Zbl 1277.90090 Numer. Algorithms 62, No. 1, 79-113 (2013). Reviewer: Didier Henrion (Toulouse) MSC: 90C22 PDFBibTeX XMLCite \textit{L. Han} et al., Numer. Algorithms 62, No. 1, 79--113 (2013; Zbl 1277.90090) Full Text: DOI
Jin, S.; Ariyawansa, K. A.; Zhu, Y. Homogeneous self-dual algorithms for stochastic semidefinite programming. (English) Zbl 1277.90092 J. Optim. Theory Appl. 155, No. 3, 1073-1083 (2012). Reviewer: Didier Henrion (Toulouse) MSC: 90C22 90C15 PDFBibTeX XMLCite \textit{S. Jin} et al., J. Optim. Theory Appl. 155, No. 3, 1073--1083 (2012; Zbl 1277.90092) Full Text: DOI
Machacek, John; Jibrin, Shafiu An interior point method for solving semidefinite programs using cutting planes and weighted analytic centers. (English) Zbl 1254.90155 J. Appl. Math. 2012, Article ID 946893, 21 p. (2012). MSC: 90C22 90C51 90C57 PDFBibTeX XMLCite \textit{J. Machacek} and \textit{S. Jibrin}, J. Appl. Math. 2012, Article ID 946893, 21 p. (2012; Zbl 1254.90155) Full Text: DOI
Simon, Jaan-Willem; Weichert, Dieter Shakedown analysis with multidimensional loading spaces. (English) Zbl 1379.74028 Comput. Mech. 49, No. 4, 477-485 (2012). MSC: 74S30 74C05 PDFBibTeX XMLCite \textit{J.-W. Simon} and \textit{D. Weichert}, Comput. Mech. 49, No. 4, 477--485 (2012; Zbl 1379.74028) Full Text: DOI
Engau, Alexander; Anjos, Miguel F.; Vannelli, Anthony On handling cutting planes in interior-point methods for solving semi-definite relaxations of binary quadratic optimization problems. (English) Zbl 1242.90193 Optim. Methods Softw. 27, No. 3, 539-559 (2012). MSC: 90C27 90C22 90C51 PDFBibTeX XMLCite \textit{A. Engau} et al., Optim. Methods Softw. 27, No. 3, 539--559 (2012; Zbl 1242.90193) Full Text: DOI
Fang, Liang; Feng, Zengzhe A smoothing Newton-type method for second-order cone programming problems based on a new smoothing Fischer-Burmeister function. (English) Zbl 1401.90152 Comput. Appl. Math. 30, No. 3, 569-588 (2011). MSC: 90C25 90C30 90C51 65K05 65Y20 PDFBibTeX XMLCite \textit{L. Fang} and \textit{Z. Feng}, Comput. Appl. Math. 30, No. 3, 569--588 (2011; Zbl 1401.90152) Full Text: DOI Link
Oskoorouchi, Mohammad R.; Ghaffari, Hamid R.; Terlaky, Tamás; Aleman, Dionne M. An interior point constraint generation algorithm for semi-infinite optimization with health-care application. (English) Zbl 1235.90167 Oper. Res. 59, No. 5, 1184-1197 (2011). MSC: 90C34 90C51 PDFBibTeX XMLCite \textit{M. R. Oskoorouchi} et al., Oper. Res. 59, No. 5, 1184--1197 (2011; Zbl 1235.90167) Full Text: DOI Link
Falkeborn, Rikard; Löfberg, Johan; Hansson, Anders Low-rank exploitation in semidefinite programming for control. (English) Zbl 1236.90090 Int. J. Control 84, No. 12, 1975-1982 (2011). MSC: 90C22 PDFBibTeX XMLCite \textit{R. Falkeborn} et al., Int. J. Control 84, No. 12, 1975--1982 (2011; Zbl 1236.90090) Full Text: DOI Link
Tang, Jingyong; He, Guoping; Dong, Li; Fang, Liang A smoothing Newton method for second-order cone optimization based on a new smoothing function. (English) Zbl 1229.65101 Appl. Math. Comput. 218, No. 4, 1317-1329 (2011). MSC: 65K05 90C25 90C53 90C51 PDFBibTeX XMLCite \textit{J. Tang} et al., Appl. Math. Comput. 218, No. 4, 1317--1329 (2011; Zbl 1229.65101) Full Text: DOI
de Klerk, Etienne; Dobre, Cristian; Ṗasechnik, Dmitrii V. Numerical block diagonalization of matrix \(\ast\)-algebras with application to semidefinite programming. (English) Zbl 1225.90098 Math. Program. 129, No. 1 (B), 91-111 (2011). MSC: 90C22 16Z05 PDFBibTeX XMLCite \textit{E. de Klerk} et al., Math. Program. 129, No. 1 (B), 91--111 (2011; Zbl 1225.90098) Full Text: DOI
Li, Lu; Toh, Kim-Chuan A polynomial-time inexact primal-dual infeasible path-following algorithm for convex quadratic SDP. (English) Zbl 1247.90211 Pac. J. Optim. 7, No. 1, 43-61 (2011). Reviewer: Paulo Mbunga (Kiel) MSC: 90C22 90C25 90C51 65F10 PDFBibTeX XMLCite \textit{L. Li} and \textit{K.-C. Toh}, Pac. J. Optim. 7, No. 1, 43--61 (2011; Zbl 1247.90211)
Li, Lu; Toh, Kim-Chuan An inexact interior point method for \(L_{1}\)-regularized sparse covariance selection. (English) Zbl 1208.90131 Math. Program. Comput. 2, No. 3-4, 291-315 (2010). MSC: 90C22 90C51 90C06 90C25 65F10 PDFBibTeX XMLCite \textit{L. Li} and \textit{K.-C. Toh}, Math. Program. Comput. 2, No. 3--4, 291--315 (2010; Zbl 1208.90131) Full Text: DOI
Andersen, Martin S.; Dahl, Joachim; Vandenberghe, Lieven Implementation of nonsymmetric interior-point methods for linear optimization over sparse matrix cones. (English) Zbl 1230.90006 Math. Program. Comput. 2, No. 3-4, 167-201 (2010). MSC: 90-08 90C06 90C22 90C25 90C51 PDFBibTeX XMLCite \textit{M. S. Andersen} et al., Math. Program. Comput. 2, No. 3--4, 167--201 (2010; Zbl 1230.90006) Full Text: DOI
Engau, Alexander; Anjos, Miguel F.; Vannelli, Anthony On interior-point warmstarts for linear and combinatorial optimization. (English) Zbl 1206.90215 SIAM J. Optim. 20, No. 4, 1828-1861 (2010). Reviewer: Mikhail Yu. Kokurin (Yoshkar-Ola) MSC: 90C51 90C05 90C27 65K05 PDFBibTeX XMLCite \textit{A. Engau} et al., SIAM J. Optim. 20, No. 4, 1828--1861 (2010; Zbl 1206.90215) Full Text: DOI Link
Fang, Liang A smoothing-type Newton method for second-order cone programming problems based on a new smooth function. (English) Zbl 1200.90137 J. Appl. Math. Comput. 34, No. 1-2, 147-161 (2010). MSC: 90C25 90C30 90C51 65K05 65Y20 PDFBibTeX XMLCite \textit{L. Fang}, J. Appl. Math. Comput. 34, No. 1--2, 147--161 (2010; Zbl 1200.90137) Full Text: DOI
Toh, Kim-Chuan; Yun, Sangwoon An accelerated proximal gradient algorithm for nuclear norm regularized linear least squares problems. (English) Zbl 1205.90218 Pac. J. Optim. 6, No. 3, 615-640 (2010). MSC: 90C22 90C25 90C51 65F10 PDFBibTeX XMLCite \textit{K.-C. Toh} and \textit{S. Yun}, Pac. J. Optim. 6, No. 3, 615--640 (2010; Zbl 1205.90218)
Wei, Hua; Wolkowicz, Henry Generating and measuring instances of hard semidefinite programs. (English) Zbl 1198.90317 Math. Program. 125, No. 1 (A), 31-45 (2010). MSC: 90C22 90C31 PDFBibTeX XMLCite \textit{H. Wei} and \textit{H. Wolkowicz}, Math. Program. 125, No. 1 (A), 31--45 (2010; Zbl 1198.90317) Full Text: DOI
Liu, Zhang; Vandenberghe, Lieven Interior-point method for nuclear norm approximation with application to system identification. (English) Zbl 1201.90151 SIAM J. Matrix Anal. Appl. 31(2009), No. 3, 1235-1256 (2010). MSC: 90C22 90C25 90C51 93B30 PDFBibTeX XMLCite \textit{Z. Liu} and \textit{L. Vandenberghe}, SIAM J. Matrix Anal. Appl. 31, No. 3, 1235--1256 (2010; Zbl 1201.90151) Full Text: DOI Link
Johansson, Janne Harju; Hansson, Anders An inexact interior-point method for system analysis. (English) Zbl 1226.90065 Int. J. Control 83, No. 3, 601-616 (2010). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{J. H. Johansson} and \textit{A. Hansson}, Int. J. Control 83, No. 3, 601--616 (2010; Zbl 1226.90065) Full Text: DOI Link
Pólik, Imre; Terlaky, Tamás Interior point methods for nonlinear optimization. (English) Zbl 1251.90391 Di Pillo, Gianni (ed.) Schoen, Fabio (ed.), Nonlinear optimization. Lectures given at the C.I.M.E. summer school held in Cetraro, Italy, July 1–7, 2007. Berlin: Springer (ISBN 978-3-642-11338-3/pbk; 978-3-642-11339-0/ebook). Lecture Notes in Mathematics 1989, 215-276 (2010). Reviewer: Efstratios Rappos (Aubonne) MSC: 90C51 90-01 90-06 PDFBibTeX XMLCite \textit{I. Pólik} and \textit{T. Terlaky}, Lect. Notes Math. 1989, 215--276 (2010; Zbl 1251.90391) Full Text: DOI
Ivanov, I. D.; de Klerk, E. Parallel implementation of a semidefinite programming solver based on CSDP on a distributed memory cluster. (English) Zbl 1189.90115 Optim. Methods Softw. 25, No. 3, 405-420 (2010). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{I. D. Ivanov} and \textit{E. de Klerk}, Optim. Methods Softw. 25, No. 3, 405--420 (2010; Zbl 1189.90115) Full Text: DOI Link
Sivaramakrishnan, Kartik Krishnan A parallel interior point decomposition algorithm for block angular semidefinite programs. (English) Zbl 1189.90200 Comput. Optim. Appl. 46, No. 1, 1-29 (2010). MSC: 90C51 90C22 PDFBibTeX XMLCite \textit{K. K. Sivaramakrishnan}, Comput. Optim. Appl. 46, No. 1, 1--29 (2010; Zbl 1189.90200) Full Text: DOI
Fang, Liang; He, Guoping; Sun, Li A globally convergent non-interior point algorithm with full Newton step for second-order cone programming. (English) Zbl 1212.90299 Appl. Math., Praha 54, No. 5, 447-464 (2009). MSC: 90C25 90C30 90C51 65K05 65Y20 PDFBibTeX XMLCite \textit{L. Fang} et al., Appl. Math., Praha 54, No. 5, 447--464 (2009; Zbl 1212.90299) Full Text: DOI EuDML Link
Boyd, Stephen; Diaconis, Persi; Parrilo, Pablo; Xiao, Lin Fastest mixing Markov chain on graphs with symmetries. (English) Zbl 1189.05072 SIAM J. Optim. 20, No. 2, 792-819 (2009). MSC: 05C25 20C30 60J10 60J22 65F15 90C22 90C51 PDFBibTeX XMLCite \textit{S. Boyd} et al., SIAM J. Optim. 20, No. 2, 792--819 (2009; Zbl 1189.05072) Full Text: DOI arXiv
Fang, Liang; He, Guoping; Hu, Yunhong A new smoothing Newton-type method for second-order cone programming problems. (English) Zbl 1183.65065 Appl. Math. Comput. 215, No. 3, 1020-1029 (2009). Reviewer: Efstratios Rappos (Athens) MSC: 65K05 90C25 90C51 PDFBibTeX XMLCite \textit{L. Fang} et al., Appl. Math. Comput. 215, No. 3, 1020--1029 (2009; Zbl 1183.65065) Full Text: DOI
Zymnis, Argyrios; Boyd, Stephen; Gorinevsky, Dimitry Relaxed maximum a posteriori fault identification. (English) Zbl 1161.94376 Signal Process. 89, No. 6, 989-999 (2009). MSC: 94A13 94A12 93E10 PDFBibTeX XMLCite \textit{A. Zymnis} et al., Signal Process. 89, No. 6, 989--999 (2009; Zbl 1161.94376) Full Text: DOI
Belloni, Alexandre; Freund, Robert M. Projective re-normalization for improving the behavior of a homogeneous conic linear system. (English) Zbl 1180.90181 Math. Program. 118, No. 2 (A), 279-299 (2009). MSC: 90C05 90C25 90C51 PDFBibTeX XMLCite \textit{A. Belloni} and \textit{R. M. Freund}, Math. Program. 118, No. 2 (A), 279--299 (2009; Zbl 1180.90181) Full Text: DOI Link
Gotoh, Jun-Ya; Takeda, Akiko Conditional minimum volume ellipsoid with application to multiclass discrimination. (English) Zbl 1201.90156 Comput. Optim. Appl. 41, No. 1, 27-51 (2008). Reviewer: Oliver Stein (Karlsruhe) MSC: 90C25 90C51 91B30 PDFBibTeX XMLCite \textit{J.-Y. Gotoh} and \textit{A. Takeda}, Comput. Optim. Appl. 41, No. 1, 27--51 (2008; Zbl 1201.90156) Full Text: DOI Link
Al-Homidan, Suliman Semidefinite programming for the educational testing problem. (English) Zbl 1211.90157 CEJOR, Cent. Eur. J. Oper. Res. 16, No. 3, 239-249 (2008). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{S. Al-Homidan}, CEJOR, Cent. Eur. J. Oper. Res. 16, No. 3, 239--249 (2008; Zbl 1211.90157) Full Text: DOI
Todd, M. J. Dual versus primal-dual interior-point methods for linear and conic programming. (English) Zbl 1163.90797 Math. Program. 111, No. 1-2 (B), 301-313 (2008). MSC: 90C51 90C08 PDFBibTeX XMLCite \textit{M. J. Todd}, Math. Program. 111, No. 1--2 (B), 301--313 (2008; Zbl 1163.90797) Full Text: DOI Link
Anjos, Miguel F.; Burer, Samuel On handling free variables in interior-point methods for conic linear optimization. (English) Zbl 1165.90682 SIAM J. Optim. 18, No. 4, 1310-1325 (2007). MSC: 90C51 90C22 90C05 65K05 PDFBibTeX XMLCite \textit{M. F. Anjos} and \textit{S. Burer}, SIAM J. Optim. 18, No. 4, 1310--1325 (2007; Zbl 1165.90682) Full Text: DOI
Al-Homidan, S. Approximate Toeplitz matrix problem using semidefinite programming. (English) Zbl 1146.90045 J. Optim. Theory Appl. 135, No. 3, 583-598 (2007). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{S. Al-Homidan}, J. Optim. Theory Appl. 135, No. 3, 583--598 (2007; Zbl 1146.90045) Full Text: DOI
Toh, K. C.; Tütüncü, R. H.; Todd, M. J. Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems. (English) Zbl 1136.90026 Pac. J. Optim. 3, No. 1, 135-164 (2007). Reviewer: Didier Henrion (Toulouse) (MR2294049) MSC: 90C22 90C51 65K10 PDFBibTeX XMLCite \textit{K. C. Toh} et al., Pac. J. Optim. 3, No. 1, 135--164 (2007; Zbl 1136.90026)
Borchers, Brian; Young, Joseph G. Implementation of a primal-dual method for SDP on a shared memory parallel architecture. (English) Zbl 1179.90256 Comput. Optim. Appl. 37, No. 3, 355-369 (2007). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{B. Borchers} and \textit{J. G. Young}, Comput. Optim. Appl. 37, No. 3, 355--369 (2007; Zbl 1179.90256) Full Text: DOI
Kobayashi, Kazuhiro; Nakata, Kazuhide; Kojima, Masakazu A conversion of an SDP having free variables into the standard form SDP. (English) Zbl 1146.90492 Comput. Optim. Appl. 36, No. 2-3, 289-307 (2007). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{K. Kobayashi} et al., Comput. Optim. Appl. 36, No. 2--3, 289--307 (2007; Zbl 1146.90492) Full Text: DOI
Al-Homidan, Suliman Solving Hankel matrix approximation problem using semidefinite programming. (English) Zbl 1117.65083 J. Comput. Appl. Math. 202, No. 2, 304-314 (2007). Reviewer: Efstratios Rappos (Athens) MSC: 65K05 90C22 90C51 65F30 PDFBibTeX XMLCite \textit{S. Al-Homidan}, J. Comput. Appl. Math. 202, No. 2, 304--314 (2007; Zbl 1117.65083) Full Text: DOI
Freund, Robert M.; Ordóñez, Fernando; Toh, Kim-Chuan Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems. (English) Zbl 1278.90447 Math. Program. 109, No. 2-3 (B), 445-475 (2007). MSC: 90C51 90C22 PDFBibTeX XMLCite \textit{R. M. Freund} et al., Math. Program. 109, No. 2--3 (B), 445--475 (2007; Zbl 1278.90447) Full Text: DOI
Sueyoshi, Toshiyuki; Sekitani, Kazuyuki Computational strategy for Russell measure in DEA: second-order cone programming. (English) Zbl 1114.90073 Eur. J. Oper. Res. 180, No. 1, 459-471 (2007). MSC: 90C08 90C22 90C51 PDFBibTeX XMLCite \textit{T. Sueyoshi} and \textit{K. Sekitani}, Eur. J. Oper. Res. 180, No. 1, 459--471 (2007; Zbl 1114.90073) Full Text: DOI
Cai, Zhi; Toh, Kim-Chuan Solving second order cone programming via a reduced augmented system approach. (English) Zbl 1128.90045 SIAM J. Optim. 17, No. 3, 711-737 (2006). MSC: 90C20 90C22 90C51 65K05 PDFBibTeX XMLCite \textit{Z. Cai} and \textit{K.-C. Toh}, SIAM J. Optim. 17, No. 3, 711--737 (2006; Zbl 1128.90045) Full Text: DOI Link
Alshahrani, Mohammed M.; Al-Homidan, Suliman S. Mixed semidefinite and second-order cone optimization approach for the Hankel matrix approximation problem. (English) Zbl 1136.49023 Nonlinear Dyn. Syst. Theory 6, No. 3, 211-224 (2006). MSC: 49M15 90C22 PDFBibTeX XMLCite \textit{M. M. Alshahrani} and \textit{S. S. Al-Homidan}, Nonlinear Dyn. Syst. Theory 6, No. 3, 211--224 (2006; Zbl 1136.49023)
Roh, Tae; Vandenberghe, Lieven Discrete transforms, semidefinite programming, and sum-of-squares representations of nonnegative polynomials. (English) Zbl 1131.90039 SIAM J. Optim. 16, No. 4, 939-964 (2006). MSC: 90C22 90C25 PDFBibTeX XMLCite \textit{T. Roh} and \textit{L. Vandenberghe}, SIAM J. Optim. 16, No. 4, 939--964 (2006; Zbl 1131.90039) Full Text: DOI Link
Krishnan, Kartik; Terlaky, Tamás Interior point and semidefinite approaches in combinatorial optimization. (English) Zbl 1098.90089 Avis, David (ed.) et al., Graph theory and combinatorial optimization. New York, NY: Springer (ISBN 0-387-25591-5/hbk; 0-387-25592-3/e-book). GERAD 25th Anniversary Series 8, 101-157 (2005). MSC: 90C51 90-02 90C05 90C22 90C27 90C57 90C59 PDFBibTeX XMLCite \textit{K. Krishnan} and \textit{T. Terlaky}, GERAD 25th Anniv. Ser. 8, 101--157 (2005; Zbl 1098.90089)
Goldfarb, D.; Scheinberg, K. Product-form Cholesky factorization in interior point methods for second-order cone programming. (English) Zbl 1079.90157 Math. Program. 103, No. 1 (A), 153-179 (2005). MSC: 90C51 PDFBibTeX XMLCite \textit{D. Goldfarb} and \textit{K. Scheinberg}, Math. Program. 103, No. 1 (A), 153--179 (2005; Zbl 1079.90157) Full Text: DOI
Todd, Michael J. Detecting infeasibility in infeasible-interior-point methods for optimization. (English) Zbl 1142.90499 Cucker, Felipe (ed.) et al., Foundations of computational mathematics: Minneapolis 2002 (FoCM 2002). Selected papers based on the plenary talks presented at FoCM 2002, Minneapolis, MN, USA, August 5–14, 2002. Cambridge: Cambridge University Press (ISBN 0-521-54253-7/pbk). London Mathematical Society Lecture Note Series 312, 157-192 (2004). MSC: 90C51 65K05 90C05 PDFBibTeX XMLCite \textit{M. J. Todd}, Lond. Math. Soc. Lect. Note Ser. 312, 157--192 (2004; Zbl 1142.90499)
Kuo, Yu-Ju; Mittelmann, Hans D. Interior point methods for second-order cone programming and OR applications. (English) Zbl 1084.90046 Comput. Optim. Appl. 28, No. 3, 255-285 (2004). MSC: 90C51 90C05 90C25 PDFBibTeX XMLCite \textit{Y.-J. Kuo} and \textit{H. D. Mittelmann}, Comput. Optim. Appl. 28, No. 3, 255--285 (2004; Zbl 1084.90046) Full Text: DOI
Toh, Kim-Chuan Solving large scale semidefinite programs via an iterative solver on the augmented systems. (English) Zbl 1071.90026 SIAM J. Optim. 14, No. 3, 670-698 (2003). MSC: 90C06 90C22 90C51 65K05 PDFBibTeX XMLCite \textit{K.-C. Toh}, SIAM J. Optim. 14, No. 3, 670--698 (2003; Zbl 1071.90026) Full Text: DOI
Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results. (English) Zbl 1030.90081 Math. Program. 95, No. 2 (B), 303-327 (2003). MSC: 90C22 90C51 65K05 65F50 05C50 PDFBibTeX XMLCite \textit{K. Nakata} et al., Math. Program. 95, No. 2 (B), 303--327 (2003; Zbl 1030.90081) Full Text: DOI
Sturm, Jos F. Avoiding numerical cancellation in the interior point method for solving semidefinite programs. (English) Zbl 1030.90139 Math. Program. 95, No. 2 (B), 219-247 (2003). MSC: 90C51 90C22 PDFBibTeX XMLCite \textit{J. F. Sturm}, Math. Program. 95, No. 2 (B), 219--247 (2003; Zbl 1030.90139) Full Text: DOI
Krishnan, Kartik; Mitchell, John E. Semi-infinite linear programming approaches to semidefinite programming problems. (English) Zbl 1028.65066 Pardalos, Panos (ed.) et al., Novel approaches to hard discrete optimization. Providence, RI: American Mathematical Society (AMS). Fields Inst. Commun. 123-142 (2003). MSC: 65K05 90C10 90C51 90C05 90C06 90C22 90C27 90C34 90C57 PDFBibTeX XMLCite \textit{K. Krishnan} and \textit{J. E. Mitchell}, Fields Inst. Commun. 123--142, 123--142 (2003; Zbl 1028.65066)
Sturm, Jos F. Implementation of interior point methods for mixed semidefinite and second order cone optimization problems. (English) Zbl 1032.90021 Optim. Methods Softw. 17, No. 6, 1105-1154 (2002). MSC: 90C22 90C51 90C20 PDFBibTeX XMLCite \textit{J. F. Sturm}, Optim. Methods Softw. 17, No. 6, 1105--1154 (2002; Zbl 1032.90021) Full Text: DOI
Peng, Jiming; Roos, Cornelis; Terlaky, Tamás Self-regularity: a new paradigm for primal-dual interior-point algorithms. (English) Zbl 1136.90045 Princeton Series in Applied Mathematics. Princeton, NJ: Princeton University Press (ISBN 0-691-09193-5/pbk; 0-691-09192-7/hbk). xv, 185 p. (2002). MSC: 90C51 90-02 90C05 PDFBibTeX XMLCite \textit{J. Peng} et al., Self-regularity: a new paradigm for primal-dual interior-point algorithms. Princeton, NJ: Princeton University Press (2002; Zbl 1136.90045)
Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki Lagrangian dual interior-point methods for semidefinite programs. (English) Zbl 1035.90054 SIAM J. Optim. 12, No. 4, 1007-1031 (2002). MSC: 90C22 90C51 90C53 65F10 49N15 49M29 PDFBibTeX XMLCite \textit{M. Fukuda} et al., SIAM J. Optim. 12, No. 4, 1007--1031 (2002; Zbl 1035.90054) Full Text: DOI
De Klerk, Etienne Aspects of semidefinite programming. Interior point algorithms and selected applications. (English) Zbl 0991.90098 Applied Optimization. 65. Dordrecht: Kluwer Academic Publishers. xvi, 283 p. (2002). Reviewer: Jan-Joachim Rückmann (Ilmenau) MSC: 90C22 90-02 90C51 PDFBibTeX XMLCite \textit{E. De Klerk}, Aspects of semidefinite programming. Interior point algorithms and selected applications. Dordrecht: Kluwer Academic Publishers (2002; Zbl 0991.90098)
Zhang, Shao-Liang; Nakata, Kazuhide; Kojima, Masakazu Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming. (English) Zbl 0994.65050 Appl. Numer. Math. 41, No. 1, 235-245 (2002). MSC: 65F35 65F10 65K05 90C22 PDFBibTeX XMLCite \textit{S.-L. Zhang} et al., Appl. Numer. Math. 41, No. 1, 235--245 (2002; Zbl 0994.65050) Full Text: DOI
Toh, Kim-Chuan A note on the calculation of step-lengths in interior-point methods for semidefinite programming. (English) Zbl 0994.90105 Comput. Optim. Appl. 21, No. 3, 301-310 (2002). MSC: 90C22 90C51 PDFBibTeX XMLCite \textit{K.-C. Toh}, Comput. Optim. Appl. 21, No. 3, 301--310 (2002; Zbl 0994.90105) Full Text: DOI
Toh, Kim-Chuan; Kojima, Masakazu Solving some large scale semidefinite programs via the conjugate residual method. (English) Zbl 1008.90043 SIAM J. Optim. 12, No. 3, 669-691 (2002). MSC: 90C22 90C52 90C06 90C51 PDFBibTeX XMLCite \textit{K.-C. Toh} and \textit{M. Kojima}, SIAM J. Optim. 12, No. 3, 669--691 (2002; Zbl 1008.90043) Full Text: DOI
de Klerk, E.; Peng, J.; Roos, C.; Terlaky, T. A scaled Gauss–Newton primal-dual search direction for semidefinite optimization. (English) Zbl 1001.65060 SIAM J. Optim. 11, No. 4, 870-888 (2001). Reviewer: N.Djuranović-Miličić (Beograd) MSC: 65K05 90C22 PDFBibTeX XMLCite \textit{E. de Klerk} et al., SIAM J. Optim. 11, No. 4, 870--888 (2001; Zbl 1001.65060) Full Text: DOI