Generalized Convexity, Generalized Monotonicity: Recent Results (Nonconvex Optimization and Its Applications (closed))

The geometrical structure induced by convexity in mathematical programming has many useful properties: continuity and differentiability of the functions, separability and optimality conditions, duality, sensibility of the optimal solutions, etc. Several of the most interesting ones are preserved when convexity is relaxed in quasiconvexity or pseudoconvexity (a function is quasi-convex if its lower level sets are convex). This is still the case for variational inequalities problems when the classical monotonicity assumption on the map is relaxed in quasimonotonicity or pseudomonotonicity. This volume contains 23 selected lectures presented at the most recent international symposium on generalized convexity. It provides an up-to-date review of recent developments. Audience: The book will be of value to researchers and students working in economics, mathematical programming, operations research, management sciences, equilibrium problems, engineering and probability.