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Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

Maryam Saadati, Morteza Oveisiha

Abstract

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of (CUP) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond-Weir-type robust dual problem to the primal problem (CUP), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.

Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications

Abstract

This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of (CUP) in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond-Weir-type robust dual problem to the primal problem (CUP), and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.
Paper Structure (5 sections, 18 theorems, 121 equations)

This paper contains 5 sections, 18 theorems, 121 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Robust necessary and sufficient optimality
  4. Robust duality
  5. Applications

Key Result

Lemma 2.1

Let $y^{*} \in Y^{*}$, and let $f : X \to Y$ be Lipschitz continuous around $\bar{x} \in X$. We have

Theorems & Definitions (44)

  • Remark 1.1
  • Definition 1.1
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Theorem 3.1
  • Theorem 3.2
  • ...and 34 more