On constrained optimization with nonconvex regularization

Abstract

In many engineering applications, it is necessary to minimize smooth functions plus penalty (or regularization) terms that violate smoothness and convexity. Specific algorithms for this type of problems are available in recent literature. Here, a smooth reformulation is analyzed and equivalence with the original problem is proved both from the points of view of global and local optimization. Moreover, for the cases in which the objective function is much more expensive than the constraints, model-intensive algorithms, accompanied by their convergence and complexity theories, are introduced. Finally, numerical experiments are presented.