A proximal method for composite minimization
This work addresses the need for efficient algorithms for a broad class of composite optimization problems, but the results are preliminary and the novelty is incremental.
The paper proposes a proximal method for minimizing composite functions involving convex or prox-regular functions composed with smooth vector functions, demonstrating global convergence and active manifold identification, with promising preliminary results on convex and nonconvex problems.
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term. Properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem. Preliminary computational results on both convex and nonconvex examples are promising.