Name
Title | ||
|---|---|---|
A Regularized Semi-Smooth Newton Method with Projection Steps for Composite Convex Programs. |
Abstract | ||
|---|---|---|
The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: (1) Many well-known operator splitting methods, such as forward–backward splitting and Douglas–Rachford splitting, actually define a fixed-point mapping; (2) The optimal solutions of the composite convex program and the solutions of a system of nonlinear equations derived from the fixed-point mapping are equivalent. Solving this kind of system of nonlinear equations enables us to develop second-order type methods. These nonlinear equations may be non-differentiable, but they are often semi-smooth and their generalized Jacobian matrix is positive semidefinite due to monotonicity. By combining with a regularization approach and a known hyperplane projection technique, we propose an adaptive semi-smooth Newton method and establish its convergence to global optimality. Preliminary numerical results on \(\ell _1\)-minimization problems demonstrate that our second-order type algorithms are able to achieve superlinear or quadratic convergence. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10915-017-0624-3 | J. Sci. Comput. |
Keywords | Field | DocType |
Composite convex programs, Operator splitting methods, Proximal mapping, Semi-smoothness, Newton method, 90C30, 65K05 | Monotonic function,Mathematical optimization,Nonlinear system,Matrix (mathematics),Positive-definite matrix,Generalized Jacobian,Regularization (mathematics),Rate of convergence,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
76 | 1 | 0885-7474 |
Citations | PageRank | References |
4 | 0.40 | 25 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Xiantao Xiao | 1 | 24 | 4.09 |
| Yongfeng Li | 2 | 4 | 0.40 |
| Zaiwen Wen | 3 | 934 | 40.20 |
| Liwei Zhang | 4 | 146 | 31.69 |