Generalized Geometric Programming with Applications

During the grant period the authors research efforts has been concentrated in five major directions 1 the effective formulation and study of two important optimization problems and two important equilibrium problems as generalized geometric programming problems, 2 an investigation of the relations between suboptimization and parameter deletion, including the relations between ordinary duality, geometric duality, and Rockafellar duality, 3 an investigation of the relations between the fixed point problem and the geometric complementarity problem a generalization of the ordinary complementarity problem, 4 an extension of the classical existence theorems for both the fixed point problem and the variational inequality problem, to deal with the geometric complementarity problem, 5 the preparation of a book that unifies and contrasts ordinary programming theory, geometric programming theory, parametric programming theory, ordinary complementarity theory, geometric complementarity theory, fixed point theory, and variational inequality theory while showing how each of these theories supplies different insights into various important optimization problems and equilibrium problems. KR