Global sufficient optimality conditions for a special cubic minimization problem
type: Item
instance of: scholarly article
title: Global sufficient optimality conditions for a special cubic minimization problem
zbMATH Open document ID: 1264.90163
DOI: 10.1155/2012/871741
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by \textit{V. Jeyakumar, A. M. Rubinov} and \textit{Z. Y. Wu} [J. Glob. Optim. 36, No.~3, 471--481 (2006; Zbl 1131.90060). The present conditions generalize the results developed in [Zbl 1131.90060] where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in [Zbl 1131.90060] and \textit{Y. Wang} et al. [J. Glob. Optim. 47, No. 4, 583--595 (2010; Zbl 1228.90088)]. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6173661
Wikidata QID: Q58912593
author: Xiaomei Zhang
author: Yanjun Wang
author: Weimin Ma
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/871741
OpenAlex ID: W2041495049
cites work: Accelerating the cubic regularization of Newton's method on convex problems
cites work: Formulation and optimization of cubic polynomial joint trajectories for industrial robots
cites work: Global optimality conditions for quadratic optimization problems with binary constraints
cites work: Global optimality conditions in maximizing a convex quadratic function under convex quadratic constraints
cites work: Conditions for global optimality. II
cites work: Global optimality conditions for nonconvex optimization
cites work: Sufficient global optimality conditions for non-convex quadratic minimization problems with box constraints
cites work: Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints
cites work: Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
cites work: Sufficient global optimality conditions for weakly convex minimization problems
cites work: Global optimality conditions for cubic minimization problem with box or binary constraints
cites work: Q3126366
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description: scientific article; zbMATH DE number 6173661