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Special Methods

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Convex Analysis and Global Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 110))

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Abstract

Many problems have a special structure which should be exploited appropriately for their efficient solution. This chapter presents in the first part special 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 the duality gap, and optimal visible point method for a particular class of problems with a visibility assumption. The second part of the chapter is devoted to the quasi-gradient duality method for global optimization and the relief indicator method for continuous optimization problems with no special structure.

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Notes

  1. 1.

    If f,g 1 ,…,g m are convex, condition (8.99) is implied by intS ≠ ∅ and by writing (8.5) in the form \( 0 \in \partial F(\alpha,\overline{x}) \) we recover the classical optimality criterion in convex programming.

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Authors and Affiliations

  1. Vietnam Academy of Science and Technology, Institute of Mathematics, Hanoi, Vietnam

    Hoang Tuy

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  1. Hoang Tuy
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Tuy, H. (2016). Special Methods. In: Convex Analysis and Global Optimization. Springer Optimization and Its Applications, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-31484-6_8

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