In this work we present TRFD, a derivative-free trust-region method based on finite differences for minimizing composite functions of the form \(f(x)=h(F(x))\), where \(F\) is a black-box function assumed to have a Lipschitz continuous Jacobian, and \(h\) is a known convex Lipschitz function, possibly nonsmooth. The method approximates the Jacobian of \(F\) via forward finite … Read more
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
We present a new algorithm, called manifold sampling, for the unconstrained minimization of a nonsmooth composite function $h\circ F$ when $h$ has known structure. In particular, by classifying points in the domain of the nonsmooth function $h$ into manifolds, we adapt search directions within a trust-region framework based on knowledge of manifolds intersecting the current … Read more
We consider power networks in which it is not possible to satisfy all loads at the demand nodes, due to some attack or disturbance to the network. We formulate a model, based on AC power flow equations, to restore the network to feasibility by shedding load at demand nodes, but doing so in a way … Read more