Inexact Penalty Decomposition Methods for Optimization Problems with Geometric Constraints

This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider someĀ  situations where parts of the constraints are nonconvex and complicated, like cardinality constraints, disjunctive programs, or matrix problems involving rank constraints. By a variable duplication andĀ  decomposition strategy, … Read more

A Unifying Framework for Sparsity Constrained Optimization

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … Read more