Open AccessGeneralized (Phi, Rho)-convexity in nonsmooth vector optimization over cones
Author(s) -
Malti Kapoor,
Surjeet Kaur Suneja,
Sunila Sharma
Publication year - 2016
Publication title -
an international journal of optimization and control: theories and applications/e-an international journal of optimization and control: theories and applications
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