Generalized (Phi, Rho)-convexity in nonsmooth vector optimization over cones

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Abstract

In this paper, new classes of cone-generalized (Phi,Rho)-convex functions are introduced for a nonsmooth vector optimization problem over cones, which subsume several known studied classes. Using these generalized functions, various sufficient Karush-Kuhn-Tucker (KKT) type nonsmooth optimality conditions are established wherein Clarke's generalized gradient is used. Further, we prove duality results for both Wolfe and Mond-Weir type duals under various types of cone-generalized (Phi,Rho)-convexity assumptions.Phi,Rho

Keywords

Nonsmooth vector optimization over cones

cone-generalized (Phi

Rho)-convexity

nonsmooth optimality conditions

duality

Conflict of interest

The authors declare they have no competing interests.

References

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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing