Characterizations of the Solution Set for a Class of η pseudolinear Programming

Convexity and the generalized convexity play a very important role in mathematical economic，engineering，management science and optimization theory.This paper is concerned with the properties and characterizations of solution sets for a class of nonlinear optimizations under the invexity and generalized invexity.In this paper，we focus on the characterizations of solution sets for η pseudolinear programming by the Dini upper directional derivative and Lagrange multiplier.First，some properties are given for the nondifferentiable pseudolinear programming with constraints under the Dini upper directional derivative.And in certain conditions，the optimal solution set and feasible set is invex for such problems.Finally，some characterizations of the solution set are proved via the Dini upper directional derivative and Lagrange multiplier.