Name
Title | ||
|---|---|---|
Manifold Sampling for Optimization of Nonconvex Functions That Are Piecewise Linear Compositions of Smooth Components |
Abstract | ||
|---|---|---|
We develop a manifold sampling algorithm for the minimization of a nonsmooth composite function f (sic) psi+hoF when psi is smooth with known derivatives, h is a known, nonsmooth, piecewise linear function, and F is smooth but expensive to evaluate. The trust-region algorithm classifies points in the domain of h as belonging to different manifolds and uses this knowledge when computing search directions. Since h is known, classifying objective manifolds using only the values of F is simple. We prove that all cluster points of the sequence of the manifold sampling algorithm iterates are Clarke stationary; this holds although points evaluated by the algorithm are not assumed to be differentiable and when only approximate derivatives of F are available. Numerical results show that manifold sampling using zeroth-order information about F is competitive with algorithms that employ exact subgradient values from partial derivative f. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M114741X | SIAM JOURNAL ON OPTIMIZATION |
Keywords | Field | DocType |
manifold sampling,composite nonsmooth optimization,derivative-free optimization | Discrete mathematics,Applied mathematics,Derivative-free optimization,Minification,Sampling (statistics),Piecewise linear function,Manifold,Mathematics | Journal |
Volume | Issue | ISSN |
28 | 4 | 1052-6234 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kamil A. Khan | 1 | 43 | 6.87 |
| Jeffrey Larson | 2 | 32 | 5.46 |
| Stefan M. Wild | 3 | 481 | 31.93 |