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      On Saddle Point Theorems and Duality Theorems for Approximate Solutions of Convex Optimization Problems

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      https://www.riss.kr/link?id=A76177505

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      다국어 초록 (Multilingual Abstract)

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      ?-Saddle point theorems and e-duality theorems for several kinds of optimization problems have been studied ([3],[4],[5],[6],[7],[8]). Using Ekeland Variational Principle ([2]), Liu ([6]) formulated a Wolfe type dual problem for points near to ?-approximate solutions of a nonconvex multiobjective optimization problem, and then proved duality theorems which hold between the primal problem and the dual problem. Very recently, Dinh et al ([1]) established sequential saddle point theorems for exact solutions of convex optimization problems which hold without any constraint qualification.
      In this talk, we presented ?-saddle point theorems and ?-duality theorems for ?-approximate solutions of convex optimization problems are investigated. We give a sequential e-saddle point theorem for an ?-approxirnate solution of a convex optimization problem which holds without any constraint qualification, and then present an ?-saddle point theorem for an ?-approximate solution which holds under a weaken constraint qualification. Furthermore we formulate a Wolfe type dual problem for ?-approximate solutions for a convex optimization problem, and then using the ?-saddle point theorem, we establish duality theorems which hold between the primal problem and the dual problem.
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      ?-Saddle point theorems and e-duality theorems for several kinds of optimization problems have been studied ([3],[4],[5],[6],[7],[8]). Using Ekeland Variational Principle ([2]), Liu ([6]) formulated a Wolfe type dual problem for points near to ?-appro...

      ?-Saddle point theorems and e-duality theorems for several kinds of optimization problems have been studied ([3],[4],[5],[6],[7],[8]). Using Ekeland Variational Principle ([2]), Liu ([6]) formulated a Wolfe type dual problem for points near to ?-approximate solutions of a nonconvex multiobjective optimization problem, and then proved duality theorems which hold between the primal problem and the dual problem. Very recently, Dinh et al ([1]) established sequential saddle point theorems for exact solutions of convex optimization problems which hold without any constraint qualification.
      In this talk, we presented ?-saddle point theorems and ?-duality theorems for ?-approximate solutions of convex optimization problems are investigated. We give a sequential e-saddle point theorem for an ?-approxirnate solution of a convex optimization problem which holds without any constraint qualification, and then present an ?-saddle point theorem for an ?-approximate solution which holds under a weaken constraint qualification. Furthermore we formulate a Wolfe type dual problem for ?-approximate solutions for a convex optimization problem, and then using the ?-saddle point theorem, we establish duality theorems which hold between the primal problem and the dual problem.

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      목차 (Table of Contents)

      • ABSTRACT
      • 1. FORMULATION
      • 2. ?-SADDLE POINT THEOREMS
      • 3. ?-DUALITY THEOREMS
      • REFERENCES
      • ABSTRACT
      • 1. FORMULATION
      • 2. ?-SADDLE POINT THEOREMS
      • 3. ?-DUALITY THEOREMS
      • REFERENCES
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