Variational Inequalities And Convex Optimization

This paper is concerned with some problems of nonlinear functionalanalysis and convex optimization. In chapter one,a new constraint qualificationwhich is weaker than the Robinson constraint qualification is discussed anda second order necessary optimality condition for mathematical programmingproblems in Banach spaces is established.In chapter two, based on Fenchel duality and Fenchel-Lagrange duality,a new Farkas-type result for finite and infinite convex inequalities in infinite-dimensional spaces is obtained.In chapter three, we extend a known existence result of generalizedquasi-variational inequalities from finite dimensional to infinite-dimensionalspaces.