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- W2203781047 abstract "?-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." @default.
- W2203781047 created "2016-06-24" @default.
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- W2203781047 date "2006-05-01" @default.
- W2203781047 modified "2023-10-18" @default.
- W2203781047 title "On Saddle Point Theorems and Duality Theorems for Approximate Solutions of Convex Optimization Problems" @default.
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