An optimal bound for d.c. programs with convex constraints

Emilio Carrizosa

Mathematical Methods of Operations Research, 2001, vol. 54, issue 1, 47-51

Abstract: A well-known strategy for obtaining a lower bound on the minimum of a d.c. function f−g over a compact convex set S⊂ℝ n consists of replacing the convex function f by a linear minorant at x 0 ∈S. In this note we show that the x 0 * giving the optimal bound can be obtained by solving a convex minimization program, which corresponds to a Lagrangian decomposition of the problem. Moreover, if S is a simplex, the optimal Lagrangian multiplier can be obtained by solving a system of n + 1 linear equations. Copyright Springer-Verlag Berlin Heidelberg 2001

Keywords: Key words: d.c. programs; bounds; Lagrangian decomposition, (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/PL00003997

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