S. K. Suneja

Generalized B-vex functions and generalized B-vex programming

A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.

Generalization of preinvex and B-vex functions

A class of functions called B-preinvex functions is introduced by relaxing the definitions of preinvex and B-vex functions. Examples are given to show that there exist functions which are B-preinvex but not preinvex or B-vex or quasipreinvex. Some of the properties of B-preinvex functions are obtained.

Generalized Nonsmooth Invexity

Abstract In this paper sufficient optimality conditions and duality results are established for a nonlinear programming problem without differentiability assumption on the data wherein Clarke’s generalized gradient is used to define invexity, pβeudoinvexity and quasiinvexity for Lipβchitz functions.

Higher-order cone-pseudoconvex, quasiconvex and other related functions in vector optimization

Recently Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010) introduced higher-order cone-convex functions and used them to obtain higher-order sufficient optimality conditions and duality results for a vector optimization problem over cones. The concepts of higher-order (strongly) cone-pseudoconvex and cone-quasiconvex functions were also defined by Bhatia (Optim. Lett. doi:10.1007/s11590-010-0248-0, 2010). In this paper we introduce the notions of higher-order naturally cone-pseudoconvex, strictly cone-pseudoconvex and weakly cone-quasiconvex functions and study various interrelations between the above mentioned functions. Higher-order sufficient optimality conditions have been established by using these functions. Generalized Mond–Weir type higher-order dual is formulated and various duality results have been established under the conditions of higher-order strongly cone-pseudoconvexity and higher-order cone quasiconvexity.

Optimality and Duality Results for Bilevel Programming Problem Using Convexifactors

The paper is devoted to the applications of convexifactors to bilevel programming problem. Here we have defined ∂∗-convex, ∂∗-pseudoconvex and ∂∗-quasiconvex bifunctions in terms of convexifactors on the lines of Dutta and Chandra (Optimization 53:77–94, 2004) and Li and Zhang (J. Opt. Theory Appl. 131:429–452, 2006). We derive sufficient optimality conditions for the bilevel programming problem by using these functions, and we establish various duality results by associating the given problem with two dual problems, namely Wolfe type dual and Mond–Weir type dual.

Duality for multiobjective fractional programming problem using convexifactors

In this paper, the concept of ∂*-quasiconvexity is introduced by using convexifactors. Mond-Weir-type and Schaible-type duals are associated with a multiobjective fractional programming problem, and various duality results are established under the assumptions of ∂*-pseudoconvexity and ∂*-quasiconvexity.

Arcwise Cone Connected Functions and Optimality

In this paper, Fritz-John and Kuhn-Tucker type necessary and sufficient conditions are given for a weak minimum, a minimum and a strong minimum of a vector valued minimization problem. Mond-Weir type dual is associated and weak and strong duality results are proved by assuming the functions involved to be arcwise cone connected.

Saddle-Point Type Optimality Criteria for Optimization Problem over Cones

In this paper, concept of arcwise cone-connected mappings, *-arcwise semi differentiability, *-pseudo cone-connected mappings and *-quasi cone-connected mappings are introduced in infinite dimensional spaces. Fritz John and Kuhn-Tucker type necessary and sufficient conditions are given for a weak minimum and a minimum of the optimization problem over cones. These conditions are then used to study saddle point optimality criteria in terms of a Lagrangian function.

Generalized higher-order cone-convex functions and higher-order duality in vector optimization

In this paper, we introduce a new class of higher-order cone-convex,