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

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 con...

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Published inAn international journal of optimization and control Vol. 6; no. 1; pp. 1 - 7
Main Authors Suneja, S K, Sharma, Sunila, Kapoor, Malti
Format Journal Article
LanguageEnglish
Published Balikesir Balikesir University, Faculty of Engineering Department of Industrial Engineering 01.01.2016
Balikesir University
Subjects
cone-generalized (Phi,Rho)-convexity
Cones
Convexity
duality
Mathematical analysis
Nonlinear programming
nonsmooth optimality conditions
Nonsmooth vector optimization over cones
Optimization
Vectors (mathematics)
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Summary: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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ISSN:2146-0957
2146-5703
DOI:10.11121/ijocta.01.2016.00247