Adrian S. Lewis

A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

Let f be a continuous function on

Partially finite convex programming, part I: quasi relative interiors and duality theory

\Rl^n

Duality relationships for entropy-like minimization problems

, 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

\eps

The radius of metric regularity

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

Error Bounds for Convex Inequality Systems

\eps

Nonsmooth optimization via quasi-Newton methods

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

Convex Analysis on the Hermitian Matrices

\bar x

CONVERGENCE OF BEST ENTROPY ESTIMATES

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

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

\bar x