Brezhneva, Olga; Evtushenko, Yuri; Malkova, Vlasta; Tret’yakov, Alexey Degenerate equality constrained optimization problems and P-regularity theory. (English) Zbl 1528.90274 Olenev, Nicholas (ed.) et al., Optimization and applications. 13th international conference, OPTIMA 2022, Petrovac, Montenegro, September 26–30, 2022. Revised selected papers. Cham: Springer. Lect. Notes Comput. Sci. 13781, 18-33 (2023). MSC: 90C46 90C30 49K27 PDFBibTeX XMLCite \textit{O. Brezhneva} et al., Lect. Notes Comput. Sci. 13781, 18--33 (2023; Zbl 1528.90274) Full Text: DOI
Brezhneva, Olga; Evtushenko, Yuri G.; Tret’yakov, Alexey A. New perspective on some classical results in analysis and optimization. (English) Zbl 1501.26010 Optim. Methods Softw. 36, No. 4, 811-820 (2021). MSC: 26B10 47J07 49J53 58C15 90C30 90C46 PDFBibTeX XMLCite \textit{O. Brezhneva} et al., Optim. Methods Softw. 36, No. 4, 811--820 (2021; Zbl 1501.26010) Full Text: DOI
Evtushenko, Yuri; Malkova, Vlasta; Tret’yakov, Alexey \(p\)-regularity theory and nonlinear optimization problems. (English) Zbl 1485.49025 Jaćimović, Milojica (ed.) et al., Optimization and applications. 10th international conference, OPTIMA 2019, Petrovac, Montenegro, September 30 – October 4, 2019. Revised selected papers. Cham: Springer. Commun. Comput. Inf. Sci. 1145, 237-253 (2020). Reviewer: Savin Treanta (Bucureşti) MSC: 49K15 90C30 PDFBibTeX XMLCite \textit{Y. Evtushenko} et al., Commun. Comput. Inf. Sci. 1145, 237--253 (2020; Zbl 1485.49025) Full Text: DOI
Evtushenko, Yu. G.; Tret’yakov, A. A. Constructive generalization of classical sufficient second-order optimality conditions. (English. Russian original) Zbl 1434.90196 Dokl. Math. 100, No. 1, 372-373 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 493-495 (2019). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{Yu. G. Evtushenko} and \textit{A. A. Tret'yakov}, Dokl. Math. 100, No. 1, 372--373 (2019; Zbl 1434.90196); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 487, No. 5, 493--495 (2019) Full Text: DOI
Evtushenko, Yu. G.; Tret’yakov, A. A.; Tyrtyshnikov, E. E. New approach to Farkas’ theorem of the alternative. (English. Russian original) Zbl 1428.46002 Dokl. Math. 99, No. 2, 208-210 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 485, No. 6, 655-658 (2019). Reviewer: Stefan Cobzaş (Cluj-Napoca) MSC: 46A40 52A40 90C05 90C32 90C46 PDFBibTeX XMLCite \textit{Yu. G. Evtushenko} et al., Dokl. Math. 99, No. 2, 208--210 (2019; Zbl 1428.46002); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 485, No. 6, 655--658 (2019) Full Text: DOI
Evtushenko, Yu. G.; Tret’yakov, A. A. 2-factor Newton method for solving constrained optimization problems with a degenerate Kuhn-Tucker system. (English. Russian original) Zbl 1418.90281 Dokl. Math. 99, No. 2, 129-131 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 485, No. 1, 19-21 (2019). MSC: 90C46 PDFBibTeX XMLCite \textit{Yu. G. Evtushenko} and \textit{A. A. Tret'yakov}, Dokl. Math. 99, No. 2, 129--131 (2019; Zbl 1418.90281); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 485, No. 1, 19--21 (2019) Full Text: DOI
Evtushenko, Yu. G.; Tret’yakov, A. A. A new proof of the Kuhn-Tucker and Farkas theorems. (English. Russian original) Zbl 1408.46069 Comput. Math. Math. Phys. 58, No. 7, 1035-1039 (2018); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 7 (2018). Reviewer: Rita Pini (Milano) MSC: 46N10 90C30 90C46 PDFBibTeX XMLCite \textit{Yu. G. Evtushenko} and \textit{A. A. Tret'yakov}, Comput. Math. Math. Phys. 58, No. 7, 1035--1039 (2018; Zbl 1408.46069); translation from Zh. Vychisl. Mat. Mat. Fiz. 58, No. 7 (2018) Full Text: DOI
Bednarczuk, Ewa M.; Tretyakov, Alexey \(p\)-regular nonlinearity: tangency at singularity in degenerate optimization problems. (English) Zbl 1458.46063 Math. Methods Oper. Res. 86, No. 3, 485-500 (2017). MSC: 46N10 47J30 47N10 90C30 PDFBibTeX XMLCite \textit{E. M. Bednarczuk} and \textit{A. Tretyakov}, Math. Methods Oper. Res. 86, No. 3, 485--500 (2017; Zbl 1458.46063) Full Text: DOI
Evtushenko, Yu. G.; Tret’yakov, A. A. New perspective on the Kuhn-Tucker theorem. (English. Russian original) Zbl 1388.90110 Dokl. Math. 96, No. 2, 427-429 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 476, No. 1, 11-13 (2017). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{Yu. G. Evtushenko} and \textit{A. A. Tret'yakov}, Dokl. Math. 96, No. 2, 427--429 (2017; Zbl 1388.90110); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 476, No. 1, 11--13 (2017) Full Text: DOI
Prusinska, A.; Tret’yakov, A. A. The \(p\)-order maximum principle for an irregular optimal control problem. (English. Russian original) Zbl 1380.49024 Comput. Math. Math. Phys. 57, No. 9, 1453-1458 (2017); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 9, 1471-1476 (2017). MSC: 49K21 58C15 PDFBibTeX XMLCite \textit{A. Prusinska} and \textit{A. A. Tret'yakov}, Comput. Math. Math. Phys. 57, No. 9, 1453--1458 (2017; Zbl 1380.49024); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 9, 1471--1476 (2017) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. When the Karush-Kuhn-Tucker theorem fails: constraint qualifications and higher-order optimality conditions for degenerate optimization problems. (English) Zbl 1377.49025 J. Optim. Theory Appl. 174, No. 2, 367-387 (2017). MSC: 49K27 49N60 90C30 90C46 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, J. Optim. Theory Appl. 174, No. 2, 367--387 (2017; Zbl 1377.49025) Full Text: DOI
Prusińska, Agnieszka; Szczepanik, Ewa; Tret’yakov, Alexey A. High-order optimality conditions for degenerate variational problems. (English) Zbl 1349.78122 Carpathian J. Math. 30, No. 3, 387-394 (2014). MSC: 78M50 90C46 PDFBibTeX XMLCite \textit{A. Prusińska} et al., Carpathian J. Math. 30, No. 3, 387--394 (2014; Zbl 1349.78122)
Tret’yakov, A. A.; Szczepanik, E. Irregular optimization models and \(p\)-order Kuhn-Tucker optimality conditions. (English. Russian original) Zbl 1311.49052 J. Comput. Syst. Sci. Int. 53, No. 3, 384-391 (2014); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2014, No. 3, 86-93 (2014). MSC: 49K15 49M05 PDFBibTeX XMLCite \textit{A. A. Tret'yakov} and \textit{E. Szczepanik}, J. Comput. Syst. Sci. Int. 53, No. 3, 384--391 (2014; Zbl 1311.49052); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upr. 2014, No. 3, 86--93 (2014) Full Text: DOI
Prusińska, Agnieszka; Tret’yakov, Alexey Necessary \(p\)-th order optimality conditions for irregular Lagrange problem in calculus of variations. (English) Zbl 1308.90197 Math. Commun. 19, No. 3, 561-572 (2014). MSC: 90C46 49M37 PDFBibTeX XMLCite \textit{A. Prusińska} and \textit{A. Tret'yakov}, Math. Commun. 19, No. 3, 561--572 (2014; Zbl 1308.90197) Full Text: Link
Tret’yakov, A. A. \(p\)th-order optimality conditions in singular calculus of variations: elements of \(p\)-regularity theory. (English. Russian original) Zbl 1281.49018 Dokl. Math. 88, No. 2, 524-528 (2013); translation from Dokl. Akad. Nauk. 452, No. 2, 136-140 (2013). MSC: 49K15 49N60 PDFBibTeX XMLCite \textit{A. A. Tret'yakov}, Dokl. Math. 88, No. 2, 524--528 (2013; Zbl 1281.49018); translation from Dokl. Akad. Nauk. 452, No. 2, 136--140 (2013) Full Text: DOI
Prusińska, Agnieszka; Szczepanik, Ewa; Tret’yakov, Alexey \(p\)-th order optimality conditions for singular Lagrange problem in calculus of variations. Elements of \(p\)-regularity theory. (English) Zbl 1266.49034 Hömberg, Dietmar (ed.) et al., System modeling and optimization. 25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 12–16, 2011. Revised Selected Papers. Heidelberg: Springer (ISBN 978-3-642-36061-9/hbk; 978-3-642-36062-6/ebook). IFIP Advances in Information and Communication Technology 391, 528-537 (2013). MSC: 49K15 49N60 PDFBibTeX XMLCite \textit{A. Prusińska} et al., IFIP Adv. Inf. Commun. Technol. 391, 528--537 (2013; Zbl 1266.49034) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. An elementary proof of the Lagrange multiplier theorem in normed linear spaces. (English) Zbl 1259.90128 Optimization 61, No. 12, 1511-1517 (2012). MSC: 90C30 90C46 49K27 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, Optimization 61, No. 12, 1511--1517 (2012; Zbl 1259.90128) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. An elementary proof of the Karush-Kuhn-Tucker theorem in normed linear spaces for problems with a finite number of inequality constraints. (English) Zbl 1222.90080 Optimization 60, No. 4-6, 613-618 (2011). MSC: 90C46 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, Optimization 60, No. 4--6, 613--618 (2011; Zbl 1222.90080) Full Text: DOI
Bednarczuk, Ewa; Prusińska, Agnieszka; Tret’yakov, Alexey A. High order stability conditions for degenerate optimization problems; elements of \(p\)-regularity theory. (English) Zbl 1229.90211 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 3, 836-846 (2011). MSC: 90C31 90C30 49K27 46N10 49N60 PDFBibTeX XMLCite \textit{E. Bednarczuk} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 3, 836--846 (2011; Zbl 1229.90211) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. The \(p\)-th order optimality conditions for degenerate inequality constrained optimization problems. (English) Zbl 1247.90283 TWMS J. Pure Appl. Math. 1, No. 2, 198-223 (2010). MSC: 90C46 90C30 49K99 49N60 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, TWMS J. Pure Appl. Math. 1, No. 2, 198--223 (2010; Zbl 1247.90283)
Prusińska, Agnieszka; Tret’yakov, Alexey \(p\)-order necessary and sufficient conditions for optimality in singular calculus of variations. (English) Zbl 1237.49027 Discuss. Math., Differ. Incl. Control Optim. 30, No. 2, 269-279 (2010). MSC: 49K15 46N10 49N60 90C30 PDFBibTeX XMLCite \textit{A. Prusińska} and \textit{A. Tret'yakov}, Discuss. Math., Differ. Incl. Control Optim. 30, No. 2, 269--279 (2010; Zbl 1237.49027) Full Text: DOI
Tret’yakov, A. A. \(p\)th order Kuhn-Tucker-type optimality conditions for a singular inequality constrained optimization problem. (English. Russian original) Zbl 1211.90240 Dokl. Math. 82, No. 2, 780-783 (2010); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 434, No. 5, 591-594 (2010). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{A. A. Tret'yakov}, Dokl. Math. 82, No. 2, 780--783 (2010; Zbl 1211.90240); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 434, No. 5, 591--594 (2010) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. Come back to Lagrange. The \(p\)-factor analysis of optimality conditions. (English) Zbl 1208.49029 Numer. Funct. Anal. Optim. 31, No. 8, 871-891 (2010). MSC: 49K27 46N10 49N60 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, Numer. Funct. Anal. Optim. 31, No. 8, 871--891 (2010; Zbl 1208.49029) Full Text: DOI
Brezhneva, Olga; Tret’yakov, Alexey A. Corrigendum: optimality conditions for degenerate extremum problems with equality constraints. (English) Zbl 1201.49025 SIAM J. Control Optim. 48, No. 5, 3670-3673 (2010). MSC: 49K27 49N60 46N10 PDFBibTeX XMLCite \textit{O. Brezhneva} and \textit{A. A. Tret'yakov}, SIAM J. Control Optim. 48, No. 5, 3670--3673 (2010; Zbl 1201.49025) Full Text: DOI
Tret’yakov, A. A. Elementary proof of classical necessary optimality conditions for a mathematical programming problem with inequality constraints. (English. Russian original) Zbl 1180.49020 Dokl. Math. 79, No. 2, 243-245 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 425, No. 4, 459-461 (2009). MSC: 49K15 49N15 90C46 PDFBibTeX XMLCite \textit{A. A. Tret'yakov}, Dokl. Math. 79, No. 2, 243--245 (2009; Zbl 1180.49020); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 425, No. 4, 459--461 (2009) Full Text: DOI
Prusínska, Agnieszka; Tret’yakov, Alexey On existence of solutions to degenerate nonlinear optimization problems. (English) Zbl 1151.90048 Discuss. Math., Differ. Incl. Control Optim. 27, No. 1, 151-164 (2007). MSC: 90C30 49M05 47H10 47A50 47J05 PDFBibTeX XMLCite \textit{A. Prusínska} and \textit{A. Tret'yakov}, Discuss. Math., Differ. Incl. Control Optim. 27, No. 1, 151--164 (2007; Zbl 1151.90048) Full Text: DOI Link
Brezhneva, O. A.; Tret’yakov, A. A. P-factor-approach to degenerate optimization problems. (English) Zbl 1219.90160 Ceragioli, F. (ed.) et al., System modeling and optimization. Proceedings of the 22nd IFIP TC7 conference, July 18–22, 2005, Turin, Italy. New York, NY: Springer (ISBN 0-387-32774-6/hbk). IFIP, International Federation for Information Processing 199, 83-90 (2006). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{O. A. Brezhneva} and \textit{A. A. Tret'yakov}, IFIP, Int. Fed. Inf. Process. 199, 83--90 (2006; Zbl 1219.90160) Full Text: DOI
Brezhneva, O. A.; Tret’yakov, A. A. The \(p\)th-order optimality conditions for inequality constrained optimization problems. (English) Zbl 1224.90206 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 5-7, e1357-e1366 (2005). MSC: 90C46 PDFBibTeX XMLCite \textit{O. A. Brezhneva} and \textit{A. A. Tret'yakov}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 5--7, e1357--e1366 (2005; Zbl 1224.90206) Full Text: DOI
Tret’yakov, Alexey; Marsden, Jerrold E. Factor-analysis of nonlinear mappings: \(p\)-regularity theory. (English) Zbl 1053.58004 Commun. Pure Appl. Anal. 2, No. 4, 425-445 (2003). Reviewer: Vassil Angelov (Sofia) MSC: 58C15 58K05 35B32 37G10 49K27 46N10 49N60 90C30 65J15 PDFBibTeX XMLCite \textit{A. Tret'yakov} and \textit{J. E. Marsden}, Commun. Pure Appl. Anal. 2, No. 4, 425--445 (2003; Zbl 1053.58004) Full Text: DOI
Brezhneva, Olga A.; Tret’yakov, Alexey A. Optimality conditions for degenerate extremum problems with equality constraints. (English) Zbl 1037.49025 SIAM J. Control Optimization 42, No. 2, 729-745 (2003). MSC: 49K27 46N10 49N60 90C30 PDFBibTeX XMLCite \textit{O. A. Brezhneva} and \textit{A. A. Tret'yakov}, SIAM J. Control Optim. 42, No. 2, 729--745 (2003; Zbl 1037.49025) Full Text: DOI
Brezhneva, O. A.; Tret’yakov, A. A.; Chmura, A. Generalization of the concept of \(p\)-regularity and higher order optimality conditions. (English. Russian original) Zbl 1161.49308 Comput. Math. Math. Phys. 41, No. 2, 187-196 (2001); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 1, 207-216 (2001). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 49K27 47N10 57R45 58E05 90C48 PDFBibTeX XMLCite \textit{O. A. Brezhneva} et al., Comput. Math. Math. Phys. 41, No. 2, 187--196 (2001; Zbl 1161.49308); translation from Zh. Vychisl. Mat. Mat. Fiz. 41, No. 1, 207--216 (2001)
Korneva, I. L.; Tret’yakov, A. A. Application of factor analysis in the calculus of variations. (Russian) Zbl 1083.49500 Bereznev, V.A. (ed.) et al., Problems of modeling and analysis in decision making problems. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel’nyj Tsentr (ISBN 5-201-09764-2). 144-162 (2000). Reviewer: Zsolt Páles (MR 2002d:49026) MSC: 49K05 49J50 PDFBibTeX XMLCite \textit{I. L. Korneva} and \textit{A. A. Tret'yakov}, in: Voprosy modelirovaniya i analiza v zadachakh prinyatiya reshenij. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel'nyj Tsentr. 144--162 (2000; Zbl 1083.49500)
Brezhneva, O. A.; Tret’yakov, A. A. Methods for solving irregular optimization problems. (Russian) Zbl 1137.90708 Bereznev, V.A. (ed.) et al., Voprosy modelirovaniya i analiza v zadachakh prinyatiya reshenij. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel’nyj Tsentr (ISBN 5-201-09764-2). 51-74 (2000). MSC: 90C46 49K40 65J20 PDFBibTeX XMLCite \textit{O. A. Brezhneva} and \textit{A. A. Tret'yakov}, in: Voprosy modelirovaniya i analiza v zadachakh prinyatiya reshenij. Moscow: RAN, Rossijskaya Akademiya Nauk, Vychislitel'nyj Tsentr. 51--74 (2000; Zbl 1137.90708)
Belash, K. N.; Tret’yakov, A. A. Methods for solving degenerate problems. (English. Russian original) Zbl 0684.65051 U.S.S.R. Comput. Math. Math. Phys. 28, No. 4, 90-94 (1988); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No. 7, 1097-1102 (1988). MSC: 65H10 65K10 49K10 PDFBibTeX XMLCite \textit{K. N. Belash} and \textit{A. A. Tret'yakov}, U.S.S.R. Comput. Math. Math. Phys. 28, No. 4, 90--94 (1988; Zbl 0684.65051); translation from Zh. Vychisl. Mat. Mat. Fiz. 28, No. 7, 1097--1102 (1988) Full Text: DOI
Balash, K. N.; Tret’yakov, A. A. Methods for solving degenerate problems. (Russian) Zbl 0653.65039 Zh. Vychisl. Mat. Mat. Fiz. 28, No. 7, 1097-1102 (1988). Reviewer: F.Luban MSC: 65H10 65K10 49K10 PDFBibTeX XMLCite \textit{K. N. Balash} and \textit{A. A. Tret'yakov}, Zh. Vychisl. Mat. Mat. Fiz. 28, No. 7, 1097--1102 (1988; Zbl 0653.65039)
Denisov, D. V.; Tret’yakov, A. A. Degenerate extremal problems. Optimality conditions for the solution. (Russian) Zbl 0575.90067 Issled. Oper. ASU 24, 41-49 (1984). MSC: 90C30 49M37 49K10 PDFBibTeX XMLCite \textit{D. V. Denisov} and \textit{A. A. Tret'yakov}, Issled. Oper. ASU 24, 41--49 (1984; Zbl 0575.90067)
Tret’yakov, A. A. Necessary and sufficient conditions for optimality of P-th order. (English) Zbl 0562.49013 U.S.S.R. Comput. Math. Math. Phys. 24, No. 1, 123-127 (1984). MSC: 49K27 46B99 49J50 58C20 58E15 90C30 90C48 PDFBibTeX XMLCite \textit{A. A. Tret'yakov}, U.S.S.R. Comput. Math. Math. Phys. 24, No. 1, 123--127 (1984; Zbl 0562.49013) Full Text: DOI
Tret’yakov, A. A. Necessary and sufficient optimality conditions of p-th order. (Russian) Zbl 0537.49009 Zh. Vychisl. Mat. Mat. Fiz. 24, No. 2, 203-209 (1984). Reviewer: W.Stańczak MSC: 49K27 46B99 49J50 58C20 58E15 90C30 90C48 PDFBibTeX XMLCite \textit{A. A. Tret'yakov}, Zh. Vychisl. Mat. Mat. Fiz. 24, No. 2, 203--209 (1984; Zbl 0537.49009)