Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions

  • Sunila Sharma University of Delhi，India
  • Priyanka Yadav University of Delhi，India
DOI: https://doi.org/10.19139/soic-2310-5070-839
Keywords: Vector optimization, Cones, second-order cone-semipseudoconvexity (semiquasiconvexity), Second-order Optimality, Duality

Abstract

Recently, Suneja et al. [26] introduced new classes of second-order cone-(\eta; \xi)-convex functions along with their generalizations and used them to prove second-order Karush–Kuhn–Tucker (KKT) type optimality conditions and duality results for the vector optimization problem involving first-order differentiable and second-order directionally differentiable functions. In this paper, we move one step ahead and study a nonsmooth vector optimization problem wherein the functions involved are first and second-order directionally differentiable. We introduce new classes of nonsmooth second-order cone-semipseudoconvex and nonsmooth second-order cone-semiquasiconvex functions in terms of second-order directional derivatives. Second-order KKT type sufficient optimality conditions and duality results for the same problem are proved using these functions.

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Published
2020-09-26
How to Cite
Sharma, S., & Yadav, P. (2020). Nonsmooth Vector Optimization Problem Involving Second-Order Semipseudo, Semiquasi Cone-Convex Functions. Statistics, Optimization & Information Computing, 9(2), 383-398. https://doi.org/10.19139/soic-2310-5070-839
Issue
Vol 9 No 2 (2021)
Section
Research Articles
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