Some Theories For The Generalized Convexity Programming And Algoeithm Research Of Constrained Linear Complementrity

In this thesis, we study the non-smooth optimization problem where the objective function and constrained functions are all locally Lipschitzian functions. The thesis includes the generalized invexity of locally Lipschitzian functions; the generalized invariant monotonicity of set-value maps and the relationships between the generalized invariant monotonicity of convexificators and the generalized invexity of nonsmooth functions; the optimality necessary and sufficient conditions for nonlinear programmings mixed dual theory; Lagrange saddle point theory.Using invex functions introduced Hanson, the generalized convexity of nonsmooth functions and generalized monotonicity of set-valued maps are further extended. The relationships between the generalized invariant monotonicity of convexificators and the generalized invexity of nonsmooth functions are established.We establish the first-order optimality necessary and sufficient conditions for non-smooth multi-objective programming, which generalizes the existing results.we propose an constrained minimization problem method to solve the generalized linear complementarity problem over a polyhedral cone (GLCP) by constructing a strictly convex constrained quadratic programming, and establish the global error bound for the GLCP based on which establish its global convergence. Some numerical experiments of the method are also reported in this paper.