OPTIMALITY AND DUALITY IN NONLINEAR PROGRAMMING INVOLVING ρ-SEMILOCALLY b-PREINVEX AND RELATED FUNCTIONS

摘要

The concepts of ρ-semilocally b-preinvex, ρ-semilocally explicitly b-preinvex, ρ-semilocally quasi b-preinvex, ρ-semilocally pseudo b-preinvex and ρ-semilocally strongly pseudo b-preinvex functions are introduced as a generalization of ρ-semilocally convex, semilocally preinvex, ρ-semilocally b-vex, semilocally b-preinvex and related functions. A nonlinear programming problem is considered, where the functions involved are η-semidifferentiable. Fritz John and Karush-Kuhn-Tucker types necessary optimality conditions are obtained. Moreover, a result concerning sufficiency of optimality conditions is given. Wolfe and Mond-Weir types duality results are formulated in terms of η-semidifferentials. These results are given using the concepts introduced.