Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions

Li, Shengjie; Xu, Yanhong; You, Manxue; Zhu, Shengkun

doi:10.1007/s10957-018-1247-z

Cited by 16 publications

(2 citation statements)

References 52 publications

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“…Some deep connections among aspects, such as duality, gap functions, error bounds, that might be not evident from other perspective can be revealed by this approach; see [40,41,42]. For more details, we refer to [43,44,45] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Weak separation functions constructed by Gerstewitz and topical functions with applications in conjugate duality

2023

J. Nonlinear Var. Anal.

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This paper aims to construct some nonlinear weak separation functions in image space analysis by virtue of the Gerstewitz and topical functions. Then, applying these separation functions, a framework of conjugate type duality for constrained vector optimization problems is introduced. The primal problem is scalarized and then the separation functions are applied to give a scalar dual problem. Meanwhile, equivalent characterizations of the zero duality gap as well as the strong duality are established via subdifferential calculus, separation properties, and saddle point assertions.

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Section: Introductionmentioning

confidence: 99%

Weak separation functions constructed by Gerstewitz and topical functions with applications in conjugate duality

2023

J. Nonlinear Var. Anal.

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“…The ISA has shown to be a useful tool in unifying several fields of the mathematical optimization theory and to allow one to find new results. After 2005, there have been lots of theoretical results based on the ISA, including optimality conditions, duality, penalty methods, regularity and gap functions, developed; see, e.g., [2,10,16,17,[33][34][35][36][40][41][42][43]45,50,53,55,56].…”

Section: Introductionmentioning

confidence: 99%

Image Space Analysis for Set Optimization Problems with Applications

Zhou

Zhu

2021

J Optim Theory Appl

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In this paper, we consider a set optimization problem with a partial order relation, which is defined by Minkowski difference. By using the image space analysis, we establish the relationships among the set optimization problem, a vector optimization problem and a set-valued optimization with vector criterion related to the image of the set optimization problem. In addition, two nonlinear regular weak separation functions are proposed for the set optimization problem. Based on the two nonlinear regular weak separation functions, saddle point sufficient optimality conditions, gap functions and error bounds for the set optimization problem, are obtained. Finally, we explore some applications of the obtained results to investigate robust multi-objective optimization problems and verify the validity of the results in shortest path problems with data uncertainty and multi-criteria traffic network equilibrium problems with interval-valued cost functions.

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Strong duality for standard convex programs

Kortanek

Zhang

2021

Math Meth Oper Res

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Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions

Cited by 16 publications

References 52 publications

Weak separation functions constructed by Gerstewitz and topical functions with applications in conjugate duality

Weak separation functions constructed by Gerstewitz and topical functions with applications in conjugate duality

Image Space Analysis for Set Optimization Problems with Applications

Strong duality for standard convex programs

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