Invex Functions and Optimization

The theory of Optimization has been increasingly significant in the progress of science and technology for the past centuries. Convex optimization problems and some of their generalizations have become very popular since the last few decades due to some findings regarding the existence of global optimal solution of such problems. One of the most important generalizations of convex functions is the invex functions, proposed by M. A. Hanson and named by B. D. Craven in 1981.The introduction of invex functions has weakened the class of optimization problems for which every stationary point is a global optima. This work is an attempt to study optimization problems involving invex functions posed in an arbitrary Hilbert space and to further weaken the class of optimization problems for which every stationary point is a global optima and Kuhn-Tucker sufficiency holds.