Approximate solutions of multiobjective optimization problems
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This paper provides some new results on approximate Pareto solutions of a multiobjective optimization problem involving nonsmooth functions. We establish Fritz-John type necessary conditions and sufficient conditions for approximate Pareto solutions of such a problem. As a consequence, we obtain Fritz-John type necessary conditions for (weakly) Pareto solutions of the considered problem by exploiting the corresponding results of the approximate Pareto solutions. In addition, we state a dual problem formulated in an approximate form to the reference problem and explore duality relations between them.
KeywordsApproximate solutions Optimality conditions Duality Fuzzy form Mordukhovich/limiting subdifferential Multiobjective optimization
Mathematics Subject Classification41A65 49K99 65K10 90C29 90C46
The authors would like to thank the referees for valuable comments and suggestions.
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