Derivative-Free Robust Optimization by Outer Approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We … Read more

Manifold Sampling for Optimization of Nonconvex Functions that are Piecewise Linear Compositions of Smooth Components

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 … Read more