TECHNIQUES OF VARIATIONAL ANALYSIS

By MARK THOMPSON

CONTENTS INTRODUCTION NOTATION EXERCISES VARIATIONAL PRINCIPLES EKELAND VARIATIONAL PRINCIPLES GEOMETRIC FORMS OF THE VARIATIONAL PRINCIPLE APPLICATIONS TO FIXED POINT THEOREMS FINITE DIMENSIONAL VARIATIONAL PRINCIPLES BORWEIN–PREISS VARIATIONAL PRINCIPLES VARIATIONAL TECHNIQUES IN SUBDI?ERENTIAL THEORY THE FR´ECHET SUBDI?ERENTIAL AND NORMAL CONE NONLOCAL SUM RULE AND VISCOSITY SOLUTIONS LOCAL SUM RULES AND CONSTRAINED MINIMIZATION MEAN VALUE THEOREMS AND APPLICATIONS CHAIN RULES AND LYAPUNOV FUNCTIONS MULTIDIRECTIONAL MVI AND SOLVABILITY EXTREMAL PRINCIPLES VARIATIONAL TECHNIQUES IN CONVEX ANALYSIS CONVEX FUNCTIONS AND SETS SUBDI?ERENTIAL SANDWICH THEOREMS AND CALCULUS FENCHEL CONJUGATE CONVEX FEASIBILITY PROBLEMS DUALITY INEQUALITIES FOR SANDWICHED FUNCTIONS ENTROPY MAXIMIZATION VARIATIONAL TECHNIQUES AND MULTIFUNCTIONS MULTIFUNCTIONS SUBDI?ERENTIALS AS MULTIFUNCTIONS DISTANCE FUNCTIONS CODERIVATIVES OF MULTIFUNCTIONS IMPLICIT MULTIFUNCTION THEOREMS VARIATIONAL PRINCIPLES IN NONLINEAR FUNCTIONAL ANALYSIS SUBDI?ERENTIAL AND ASPLUND SPACES NONCONVEX SEPARATION THEOREMS STEGALL VARIATIONAL PRINCIPLES MOUNTAIN PASS THEOREM ONE-PERTURBATION VARIATIONAL PRINCIPLES VARIATIONAL TECHNIQUES IN THE PRESENCE OF SYMMETRY NONSMOOTH FUNCTIONS ON SMOOTH MANIFOLDS MANIFOLDS OF MATRICES AND SPECTRAL FUNCTIONS CONVEX SPECTRAL FUNCTIONS REFERENCES