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General Methods

In: Convex Analysis and Global Optimization

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  • Hoang Tuy

    (Institute of Mathematics)

Abstract

Methods for solving global optimization problems combine in different ways some basic techniques of partitioning, bounding, cutting, and approximation 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 property of exhaustiveness which is crucial for the convergence of methods using partitioning. Section 6.2 presents a prototype BB procedure along with its convergence condition expressed in terms of the partitioning and bounding operations. Finally Sect. 6.3 presents a prototype outer approximation procedure. The latter consists in iteratively building a sequence of cuts determining a sequence of relaxed problems whose global optimal solutions will eventually converge to a global optimal solution of the original problem.

Suggested Citation

  • Hoang Tuy, 2016. "General Methods," Springer Optimization and Its Applications, in: Convex Analysis and Global Optimization, edition 2, chapter 0, pages 151-165, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31484-6_6
    DOI: 10.1007/978-3-319-31484-6_6
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