Vasile Preda

On efficiency and duality for multiobjective programs

Abstract For a multiobjective nonlinear program which involved inequality and equality constraints, Wolfe, Mond-Weir, and general Mond-Weir type duals are formulated and the concept of efficiency (Pareto optimum) is used to state some duality results under generalized (F, ϱ)-convexity assumptions.

On constraint qualification in multiobjective optimization problems: semidifferentiable case

Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn–Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated.

Nonlinear programming with E-preinvex and local E-preinvex functions

In this paper, we extend the class of E-convex sets, E-convex and E-quasiconvex functions introduced by [Youness, E.A., 1999. E-convex sets, E-convex functions and E-convex programming. Journal of Optimization Theory and Applications 102, 439-450], respectively by [Syau, Yu-Ru, Lee, E. Stanley, 2005. Some properties of E-convex functions. Applied Mathematics Letters 18, 1074-1080] to E-invex set, E-preinvex, E-prequasiinvex and corresponding local concepts. Some properties of these classes are studied. As an application of our results, we consider the nonlinear programming problem for which, we establish that, under mild conditions, a local minimum is a global minimum.

Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions

Necessary and sufficient optimality conditions are obtained for a nonlinear fractional multiple objective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and duality results are proved using concepts of generalized semilocally preinvex functions.

Optimality and duality in nonlinear programming involving semilocally preinvex and related functions

Abstract For a nondifferentiable nonlinear programming problem, Fritz John and Kuhn-Tucker necessary optimality conditions and sufficient optimality conditions are given and duality results are stated for Wolfe’s type and Mond-Weir type duals by the concepts of semilocally quasi-preinvex and semilocally pseudo-preinvex functions.

On optimality and duality for multiobjective programming problems involving generalized d-type-I and related n-set functions

In this paper we establish some optimality and duality results under generalized convexity assumptions for a multiobjective programming problem involving generalized d-type-I and related n-set functions.

Optimality and Wolfe Duality for Multiobjective Programming Problems Involving n-set Functions

In this paper we establish some optimality and Wolfe duality results under generalized convexity assumptions for a multiobjective programming problem involving d-type-I and related n-set functions.

Generalized V-univexity type-I for multiobjective programming with n-set functions

In the last time important results in multiobjective programming involving type-I functions were obtained (Yuan et al. in: Konnov et al. (eds) Lecture notes in economics and mathematical systems, 2007; Mishra et al. An Univ Bucureşti Ser Mat, LII(2): 207–224, 2003). Following one of these ways, we study optimality conditions and generalized Mond-Weir duality for multiobjective programming involving n-set functions which satisfy appropriate generalized univexity V-type-I conditions. We introduce classes of functions called (ρ, ρ′)-V-univex type-I, (ρ, ρ′)-quasi V-univex type-I, (ρ, ρ′)-pseudo V-univex type-I, (ρ, ρ′)-quasi pseudo V-univex type-I, and (ρ, ρ′)-pseudo quasi V-univex type-I. Finally, a general frame for constructing functions of these classes is considered.

On Variational-like Inequalities with Generalized Monotone Mappings

We consider two new classes of generalized relaxed α-monotone and semimonotone functions and using the KKM technique we prove the existence of solutions for variational-like inequalities relative to these types of mappings in Banach spaces. Several examples and special cases are also considered.

On generalized convexity and duality with a square root term

We extend the duality theorems for a class of nondifferentiable problems with Mond-Weir type duals.