Existence and approximation for variational problems under uniform constraints on the gradient by power penalty

Artículo de publicación ISISin acceso a texto completoVariational problems under uniform quasi-convex constraints on the gradient are studied. Our technique consists in approximating the original problem by a one-parameter family of smooth unconstrained optimization problems. Existence of solutions to the problems under consideration is proved as well as existence of Lagrange multipliers associated to the uniform constraint; no constraint qualification condition is required. The solution-multiplier pairs are shown to satisfy an Euler-Lagrange equation and a complementarity property. Numerical experiments confirm the ability of our method to accurately compute solutions and Lagrange multipliers.Institute on Complex Engineering Systems ICMP-05-004-F CONICYT FBO16 FONDECYT 1130176 CONICYT-Chile under grant FONDECYT 312016