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On Converse Duality for Nonsmooth Optimization Problem

Gue Myung Lee, Do Sang Kim

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Abstract

Recently, Reiland [6] defined the nonsmooth invexity of Lipschitz functions and obtained the generalized Kuhn-Tucker sufficient optimality criteria, the weak duality and the strong duality for a nonlienar optimization problem (P) involving nonsmooth invex Lipschitz functions. The purpose of this brief paper, following Jeyakumar’s [4] approach, is to establish the converse duality for (P).

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What this paper is about

Recently, Reiland [6] defined the nonsmooth invexity of Lipschitz functions and obtained the generalized Kuhn-Tucker sufficient optimality criteria, the weak duality and the strong duality for a nonlienar optimization problem (P) involving nonsmooth invex Lipschitz functions. The purpose of this brief paper, following Jeyakumar’s [4] approach, is to establish the converse duality for (P).

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Recently, Reiland [6] defined the nonsmooth invexity of Lipschitz functions and obtained the generalized Kuhn-Tucker sufficient optimality criteria, the weak duality and the strong duality for a nonlienar optimization problem (P) involving nonsmooth invex Lipschitz functions. The purpose of this brief paper, following Jeyakumar’s [4] approach, is to establish the converse duality for (P).

Key concepts: Converse, Duality (order theory), Lipschitz continuity, Mathematics, Strong duality, Duality gap, Weak duality, Perturbation function

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