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DC Optimization Problems

In: Convex Analysis and Global Optimization

Author

Listed:
  • Hoang Tuy

    (Institute of Mathematics)

Abstract

This chapter presents methods and algorithms for solving the basic dc optimization problems: concave minimization under linear constraints (Sect. 7.1), 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 design calculations, location, distance geometry, and clustering. An important new result in this chapter is a surprisingly simple proof of the convergence of algorithms using ω-subdivision—a question which had remained open during two decades before being settled with quite sophisticated proofs by Locatelli (Math Program 85:593–616, 1999), Jaumard and Meyer (J Optim Theory Appl 110:119–144, 2001), and more recently Kuno and Ishihama (J Glob Optim 61:203–220, 2015). In addition, the new concept of ω-bisection by Kuno–Ishihama is introduced as a substitute for ω-subdivision.

Suggested Citation

  • Hoang Tuy, 2016. "DC Optimization Problems," Springer Optimization and Its Applications, in: Convex Analysis and Global Optimization, edition 2, chapter 0, pages 167-228, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31484-6_7
    DOI: 10.1007/978-3-319-31484-6_7
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