Second-Order Optimality Conditions in Locally Lipschitz Inequality-Constrained Multiobjective Optimization

Elena Constantin ()
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Elena Constantin: University of Pittsburgh at Johnstown

Journal of Optimization Theory and Applications, 2020, vol. 186, issue 1, No 3, 50-67

Abstract: Abstract The main goal of this paper is to give some primal and dual Karush–Kuhn–Tucker second-order necessary conditions for the existence of a strict local Pareto minimum of order two for an inequality-constrained multiobjective optimization problem. Dual Karush–Kuhn–Tucker second-order sufficient conditions are provided too. We suppose that the objective function and the active inequality constraints are only locally Lipschitz in the primal necessary conditions and only strictly differentiable in sense of Clarke at the extremum point in the dual conditions. Examples illustrate the applicability of the obtained results.

Keywords: Nonsmooth multiobjective optimization; Karush–Kuhn–Tucker dual optimality conditions; Strict local Pareto minimum of order two; Second-order efficiency conditions; 90C29; 49K27; 90C30; 90C48 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01688-9

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