Image Space Analysis to Lagrange-Type Duality for Constrained Vector Optimization Problems with Applications

Zhu, Shengkun

doi:10.1007/s10957-016-1027-6

Cited by 15 publications

(1 citation statement)

References 30 publications

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“…Using image space analysis, many crucial results of optimization theory, like necessary conditions and constraint qualifications, obtained by the classical way can be rebuilt in a new perception and even led to more general conclusions. 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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