First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives

Nguyen Dinh Tuan

Applied Mathematics and Computation, 2015, vol. 251, issue C, 300-317

Abstract: We investigate a nonsmooth vector optimization problem with a feasible set defined by a generalized inequality constraint, an equality constraint and a set constraint. Both necessary and sufficient optimality conditions of first and second-order for weak solutions and firm solutions are established in terms of Fritz-John–Lagrange multiplier rules using set-valued directional derivatives and tangent cones and second-order tangent sets. We impose steadiness and strict differentiability for first and second-order necessary conditions, respectively; stability and l-stability for first and second-order sufficient conditions, respectively. The obtained results improve or include some recent known ones. Several illustrative examples are also provided.

Keywords: Nonsmooth vector optimization; Optimality condition; Weak solution; Firm solution; Set-valued directional derivative (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:300-317

DOI: 10.1016/j.amc.2014.11.061

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