de Oliveira, Welington Target radius methods for nonsmooth convex optimization. (English) Zbl 1409.90139 Oper. Res. Lett. 45, No. 6, 659-664 (2017). Summary: We consider the target radius method of A. Ouorou [Math. Program. 119, No. 2 (A), 239–271 (2009; Zbl 1173.90009)] and propose some extensions to handle particular classes of (a) nonsmooth convex (nonlinearly) constrained optimization problems; (b) bilevel optimization problems. The given approaches generalize the well-known level bundle methods, and one of the new algorithms possesses (nearly) dimension-independent iteration complexity. Cited in 8 Documents MSC: 90C25 Convex programming 90C56 Derivative-free methods and methods using generalized derivatives Keywords:nonsmooth optimization; convex optimization; bundle methods Citations:Zbl 1173.90009 PDFBibTeX XMLCite \textit{W. de Oliveira}, Oper. Res. Lett. 45, No. 6, 659--664 (2017; Zbl 1409.90139) Full Text: DOI References: [1] Ben-Tal, A.; Nemirovski, A., Non-euclidean restricted memory level method for large-scale convex optimization, Math. Program., 102, 407-456 (2005) · Zbl 1066.90079 [2] Brannlund, U.; Kiwiel, K. C.; Lindberg, P. O., A descent proximal level bundle method for convex nondifferentiable optimization, Oper. Res. Lett., 17, 3, 121-126 (1995) · Zbl 0843.90093 [3] de Oliveira, W.; Sagastizábal, C., Level bundle methods for oracles with on demand accuracy, Optim. Methods Softw., 29, 6, 1180-1209 (2014) · Zbl 1306.90121 [4] de Oliveira, W.; Sagastizábal, C.; Lemaréchal, C., Convex proximal bundle methods in depth: a unified analysis for inexact oracles, Math. Program., 148, 241-277 (2014) · Zbl 1327.90321 [5] Elzinga, J.; Moore, T. G., A central cutting plane method for the convex programming problem, Math. Program., 8, 134-145 (1975) · Zbl 0318.90048 [6] Kiwiel, K., Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities, Math. Program., 69, 1, 89-109 (1995) · Zbl 0857.90101 [7] Lan, G., Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization, Math. Program., 149, 1, 1-45 (2015) · Zbl 1321.90104 [8] Lemaréchal, C.; Nemirovskii, A.; Nesterov, Y., New variants of bundle methods, Math. Program., 69, 1, 111-147 (1995) · Zbl 0857.90102 [9] Ouorou, A., A proximal cutting plane method using chebychev center for nonsmooth convex optimization, Math. Program., 119, 2, 239-271 (2009) · Zbl 1173.90009 [10] Solodov, M. V., A bundle method for a class of bilevel nonsmooth convex minimization problems, SIAM J. Optim., 18, 1, 242-259 (2007) · Zbl 1145.90082 [11] van Ackooij, W.; Cruz, J. B.; de Oliveira, W., A strongly convergent proximal bundle method for convex minimization in hilbert spaces, Optimization, 65, 1, 145-167 (2016) · Zbl 1334.49101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.