Article
An optimal bound for d.c. programs with convex constraints
Author/s | Carrizosa Priego, Emilio José |
Department | Universidad de Sevilla. Departamento de Estadística e Investigación Operativa |
Publication Date | 2001-04-01 |
Deposit Date | 2021-04-23 |
Published in |
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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⊂ℝn consists of replacing the convex function f by a linear minorant at x 0∈S. In this note we show that ... 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⊂ℝn 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. |
Citation | Carrizosa Priego, E.J. (2001). An optimal bound for d.c. programs with convex constraints. Mathematical Methods of Operations Research volume, 54, 47-51. |
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