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

Malti Kapoor | Zendy; S. K. Suneja | Zendy; Sunila Sharma | Zendy

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

Author(s) -

Malti Kapoor,

S. K. Suneja,

Sunila Sharma

Publication year - 2016

Publication title -

an international journal of optimization and control theories and applications (ijocta)

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.287

H-Index - 6

eISSN - 2146-5703

pISSN - 2146-0957

DOI - 10.11121/ijocta.01.2016.00247

Subject(s) - dual polyhedron , convexity , karush–kuhn–tucker conditions , mathematics , cone (formal languages) , duality (order theory) , regular polygon , convex cone , type (biology) , pure mathematics , strong duality , convex optimization , optimization problem , combinatorics , convex analysis , mathematical optimization , geometry , algorithm , ecology , financial economics , economics , biology

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

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