In this monograph the author presents the theory of duality fornonconvex approximation in normed linear spaces and nonconvex globaloptimization in locally convex spaces. Key topics include:* duality for worst approximation (i.e., the maximization of thedistance of an element to a convex set)* duality for reverse convex best approximation (i.e., the minimization ofthe distance of an element to the complement of a convex set)* duality for convex maximization (i.e., the maximization of a convexfunction on a convex set)* duality for reverse convex minimization (i.e., the minimization of aconvex function on the complement of a convex set)* duality for d.c. optimization (i.e., optimization problems involvingdifferences of convex functions).Detailed proofs of results are given, along with varied illustrations.While many of the results have been published in mathematical journals,this is the first time these results appear in book form. Inaddition, unpublished results and new proofs are provided. Thismonograph should be of great interest to experts in this and relatedfields.Ivan Singer is a Research Professor at the Simion Stoilow Institute ofMathematics in Bucharest, and a Member of the Romanian Academy. He isone of the pioneers of approximation theory in normed linear spaces, andof generalizations of approximation theory to optimization theory. Hehas been a Visiting Professor at several universities in the U.S.A.,Great Britain, Germany, Holland, Italy, and other countries, and was theprincipal speaker at an N. S. F. Regional Conference at Kent StateUniversity. He is one of the editors of the journals NumericalFunctional Analysis and Optimization (since its inception in 1979),Optimization, and Revue d'analyse num'erique et de th'eorie del'approximation. His previous books include Best Approximation inNormed Linear Spaces by Elements of Linear Subspaces (Springer 1970),The Theory of Best Approximation and Functional Analysis (SIAM 1974), Basesin Banach Spaces I, II (Springer, 1970, 1981), and Abstract Convex Analysis(Wiley-Interscience, 1997).