 General MethodsHoang Tuy
Chapter Chapter 6 in Convex Analysis and Global Optimization, 2016, pp 151-165 from Springer Abstract: 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. Keywords: OA Procedure; Outer Approximation (OA); Relaxed Problem; Nonconvex Global Optimization Problems; Conical Subdivision (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-31484-6_6 Ordering information: This item can be ordered from DOI: 10.1007/978-3-319-31484-6_6 Access Statistics for this chapter More chapters in Springer Optimization and Its Applications from Springer |
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