We investigate the coordination of groups of autonomous robots performing spatially-distributed sensing tasks. We present facility location functions from geometric optimization and study their differentiable properties. We then design distributed coordination algorithms and analyze them as nonsmooth gradient flows. The resulting control laws correspond to basic interaction behaviors between th...

The exactness of the penalization for the exact l1 penalty function method used for solving nonsmooth constrained optimization problems with both inequality and equality constraints are presented. Thus, the equivalence between the sets of optimal solutions in the nonsmooth constrained optimization problem and its associated penalized optimization problem with the exact l1 penalty function is es...

Multiband frequency domain synthesis consists in the minimization of a finite family of closed-loop transfer functions on prescribed frequency intervals. This is an algorithmically difficult problem due to its inherent nonsmoothness and nonconvexity. We extend our previous work on nonsmooth H∞ synthesis to develop a nonsmooth optimization technique to compute local solutions to multiband synthe...

This paper is concerned with the problem of learning in networks where some or all of the functions involved are not smooth. Examples of such networks are those whose neural transfer functions are piecewise-linear and those whose error function is defined in terms of the 100 norm. Up to now, networks whose neural transfer functions are piecewise-linear have received very little consideration in...

The quality measures used in information retrieval are particularly difficult to optimize directly, since they depend on the model scores only through the sorted order of the documents returned for a given query. Thus, the derivatives of the cost with respect to the model parameters are either zero, or are undefined. In this paper, we propose a class of simple, flexible algorithms, called Lambd...

We discuss two nonsmooth functions on Rn introduced by Nesterov. We show that the first variant is partly smooth in the sense of Lewis and that its only stationary point is the global minimizer. In contrast, we show that the second variant has 2n−1 Clarke stationary points, none of them local minimizers except the global minimizer, but also that its only Mordukhovich stationary point is the glo...