2021-04-232021-04-232001-04-01Carrizosa Priego, E.J. (2001). An optimal bound for d.c. programs with convex constraints. Mathematical Methods of Operations Research volume, 54, 47-51.1432-29941432-5217https://hdl.handle.net/11441/107628A 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.application/pdf4 p.engAttribution-NonCommercial-NoDerivatives 4.0 InternacionalAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Lagrangian decompositionboundsd.c. programsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/PL00003997