Convergence of convex-concave saddle functions: applications to convex programming and mechanics

Abstract It is shown that operation of partial conjugation (the partial Legendre-Fenchel transform) of bivariate convex-concave functions has bicontinuity properties with respect to the extended epi/hypo-convergence of saddle functions and the epi-convergence of the partial conjugate (convex) functions. The results are applied to study the stability of the optimal solutions and associated multipliers of convex programs, and to a couple of problems in mechanics.

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