We consider optimization problems with objective and constraint functions that may be nonconvex and nonsmooth. Problems of this type arise in important applications, many having solutions at points of nondifferentiability of the problem functions. We present a line search algorithm for situations when the objective and constraint functions are locally Lipschitz and continuously differentiable o...

Any spectral function can be written as a composition of a symmetric function f : IR 7→ IR and the eigenvalue function λ(·) : S 7→ IR, often denoted by (f ◦ λ), where S is the subspace of n×n symmetric matrices. In this paper, we present some nonsmooth analysis for such spectral functions. Our main results are: (a) (f ◦ λ) is directionally differentiable if f is semidifferentiable; (b) (f ◦ λ) ...

Emerging applications for networked and cooperative robots motivate the study of motion coordination for groups of agents. For example, it is envisioned that groups of agents will perform a variety of useful tasks including surveillance, exploration, and environmental monitoring. This paper deals with basic interactions among mobile agents such as “move away from the closest other agent” or “mo...

We consider the bilevel problem of minimizing a nonsmooth convex function over the set of minimizers of another nonsmooth convex function. Standard convex constrained optimization is a particular case in this framework, corresponding to taking the lower level function as a penalty of the feasible set. We develop an explicit bundle-type algorithm for solving the bilevel problem, where each itera...

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and gener...

In this paper, we propose a new algorithm called ModelBI by blending the Bregman iterative regularization method and model function technique for solving class of nonconvex nonsmooth optimization problems. On one hand, use technique, which is essentially first-order approximation to objective function, go beyond traditional Lipschitz gradient continuity. other generate solutions fitting certain...

Many discrete-time dynamic models of current interest are based on functions that, while generally continuous, are nonsmooth; examples include speci c multimodels, hinging hyperplane models, and hybrid systems. We consider two models for which we can vary the smoothness and examine its in uence on qualitative behavior. In the smooth regime, both models exhibit asymptotic stability for suÆcientl...

In this paper we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints (MPECs). We first show that MPEC-LICQ is not a constraint qualification for the strong (S-) stationary condition when the objective function is nonsmooth. Enhanced Fritz John conditions provide stronger necessary optimality conditions under weaker constraint qualifications. In...