Titlebook: Convex Analysis and Global Optimization; Hoang Tuy Book 2016Latest edition Springer International Publishing AG 2016 D.C. functions.convex

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General Methods by relaxation or restriction. This chapter presents two most popular general methods: branch and bound (BB) and outer approximation (OA). Section 6.1 discusses the theoretical foundations of three basic types of partitioning processes: simplicial, conical, and rectangular, with a focus on the basic

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DC Optimization Problems, concave minimization under convex constraints (Sect. 7.2), reverse convex programming (Sect. 7.3), general canonical dc optimization problem (Sect. 7.4), general robust approach to dc optimization (Sect. 7.5), and also applications of dc optimization in various fields (Sects. 7.6–7.8) such as desi

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Special Methodspecial methods adapted to special problems of dc optimization and extensions: polyhedral annexation for concave minimization and reverse convex programming, decomposition method for convex problems depending upon a multivariate parameter, including decomposition of partly convex problems by reducing

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Nonconvex Quadratic Programmingree of nonconvexity. One of the earliest significant results in this area is the celebrated S-Lemma of Yakubovich which plays a major role in the development of quadratic optimization. In this chapter, a study of nonconvex quadratic programming is provided that starts with a generalized S-Lemma esta