Line Search and Trust-Region Methods for Convex-Composite Optimization

We consider descent methods for solving non-finite valued nonsmooth convex-composite optimization problems that employ Gauss-Newton subproblems to determine the iteration update. Specifically, we establish the global convergence properties for descent methods that use a backtracking line search, a weak Wolfe line search, or a trust-region update. All of these approaches are designed to exploit the structure associated with convex-composite problems.