Manifold Sampling for Optimization of Nonconvex Functions That Are Piecewise Linear Compositions of Smooth Components
Here, we develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $$f \triangleq \psi + h \circ F$$ 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 $$\partial f$$.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- Grant/Contract Number:
- AC02-06CH11357
- OSTI ID:
- 1491737
- Journal Information:
- SIAM Journal on Optimization, Vol. 28, Issue 4; ISSN 1052-6234
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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