CONTENTS Summary

Summary. The number of computational or theoretical applications of nonlinear duality theory is small compared to the number of theoretical papers on this subject over the last decade. This study attempts to rework and extend the fundamental results of convex duality theory so as to diminish the existing obstacles to successful application. New results are also given having to do with important but usually neglected questions concerning the computational solution of a program via its dual. Several applications are made to the general theory of convex systems. The general approach is to exploit the powerful concept ofa perturbation function, thus permitting simplified proofs (no conjugate functions or fixed-point theorems are needed) and useful geometric and mathematical insights. Consideration is limited to finite-dimensional spaces