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Kamil Khan (kamilkhanmcmaster.ca) Abstract: We develop a manifold sampling algorithm for the unconstrained minimization of a nonsmooth composite function f , ψ + h ◦ F when ψ is smooth with known derivatives, h is a nonsmooth, piecewise linear function, and F is smooth but expensive to evaluate. The trustregion 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 zeroorder information is competitive with gradient sampling algorithms that are given exact gradient values. Keywords: Manifold Sampling, Composite Nonsmooth Optimization, DerivativeFree Optimization Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Nonlinear Optimization (Unconstrained Optimization ) Citation: Mathematics and Computer Science Division Preprint ANL/MCSP80010817, September 2017 Download: [PDF] Entry Submitted: 10/01/2017 Modify/Update this entry  
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