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

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