A proximal method for composite minimization
arXiv:0812.0423
Abstract
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.
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- Proximal algorithms for constrained composite optimization, with applications to solving low-rank SDPs
- A splitting proximal point method for Nash-Cournot equilibrium models involving nonconvex cost functions
- Computing proximal points of convex functions with inexact subgradients
- Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization