A difference of convex functions approach for sparse pde optimal control\n problems with nonconvex costs

2017/11/06 by Pedro Merino, Merino, Pedro, Pedro J. Muñoz‐Merino · 1 citation
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Optimization and Mathematical Programming

paper · pdf · doi:10.48550/arxiv.1711.01997

Abstract

We propose a local regularization of elliptic optimal control problems which\ninvolves the nonconvex L^q fractional penalizations in the cost function. The\nproposed \Huber type regularization allows us to formulate the PDE\nconstrained optimization formulation as a DC programming problem (difference of\nconvex functions) that is useful to obtain necessary optimality conditions and\ntackle its numerical solution by applying the well known DC algorithm used in\nnonconvex optimization problems. By this procedure we approximate the original\nproblem in terms of a consistent family of parameterized problems for which\nthere are efficient numerical methods available. Finally, we present numerical\nexperiments to illustrate our theory with different configurations associated\nto the parameters of the problem.\n

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