James V. Burke

A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

Let f be a continuous function on

Weak sharp minima in mathematical programming

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An exact penalization viewpoint of constrained optimization

, and suppose f is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which f is not differentiable. Of particular interest is the case where f is not convex, and perhaps not even locally Lipschitz, but is a function whose gradient is easily computed where it is defined. We present a practical, robust algorithm to locally minimize such functions, based on gradient sampling. No subgradient information is required by the algorithm. When f is locally Lipschitz and has bounded level sets, and the sampling radius

HIFOO - A MATLAB PACKAGE FOR FIXED-ORDER CONTROLLER DESIGN AND H∞ OPTIMIZATION

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On the identification of active constraints

is fixed, we show that, with probability 1, the algorithm generates a sequence with a cluster point that is Clarke

Optical Wavefront Reconstruction: Theory and Numerical Methods

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On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure

-stationary. Furthermore, we show that if f has a unique Clarke stationary point

A robust sequential quadratic programming method

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Calmness and exact penalization

, then the set of all cluster points generated by the algorithm converges to

A non–interior predictor–corrector path following algorithm for the monotone linear complementarity problem

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