- Manifold Sampling for Optimization of Nonconvex Functions that are Piecewise Linear Compositions of Smooth Components Kamil Khan (kamilkhanmcmaster.ca) Jeffrey Larson (jmlarsonanl.gov) Stefan M Wild (wildanl.gov) Abstract: We develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \defined \psi + h \circ F$ 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 $\partial f$. Keywords: Manifold Sampling, Composite Nonsmooth Optimization, Derivative-Free Optimization Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Mathematics and Computer Science Division Preprint ANL/MCS-P8001-0817, September 2017 Download: [PDF]Entry Submitted: 10/01/2017Entry Accepted: 10/01/2017Entry Last Modified: 04/19/2018Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.