Minimax Problems, Saddle-Functions and Duality

Abstract : Minimax problems are fundamented to nonlinear programming, because of the way constraints can be represented using Lagrange multipliers. Better ways of solving minimax problems would lead thus lead to breakthroughs in solving most other problems of optimization. The dissertation opens a new avenue to the study of minimax problems by developing a theory of dual operations on saddle- functions convex-concave functions parallel to that already known for (purely) convex functions. Results are thereby obtained concerning minimax problems which are dual to each other. It is expected that these results will find computational applications analogous to those already acclaimed in the convex case, for instance in decomposition of large-scale problems.