In a standard free end nonsmooth control problem in finite dimensional state space, a nonsmooth maximum principle is proved, in which the adjoint inclusion is sharper than the usual one. For end constrained problems, the same result holds, provided conditions ensuring local controllability are satisfied. The adjoint inclusion is expressed by means of a type of generalized gradient of the pseudo...

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem is very limited. For example, it is not known whether the proximal stochastic gradient method with constant minibatch converges to a stationary point. To tackle this issue, we develop fast st...

In this article, we consider chaotic behavior happened in nonsmooth dynamical systems. To quantify such a behavior, a computation of Lyapunov exponents for chaotic orbits of a given nonsmooth dynamical system is focused. The Lyapunov exponent is a very important concept in chaotic theory, because this quantity measures the sensitive dependence on initial conditions in dynamical systems. Therefo...

Measurement of integral non-linearity (INL) and differential non-linearity (DNL) of an A/D converter using the histogram method incurs large test time. This test time can be a significant percentage of the total test time, especially for high resolution and low sampling-speed A/D converters. This paper describes a test methodology for measuring the INL and DNL specifications of A/D converters b...

Nonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyz...

Classical canard explosion results in smooth systems require the vector field to be at least C, since canard cycles are created as the result of a Hopf bifurcation. The work on canards in nonsmooth, planar systems is recent and has thus far been restricted to piecewise-linear or piecewise-smooth Van der Pol systems, where an extremum of the critical manifold arises from the nonsmoothness. In bo...

In this paper, we design a numerical algorithm for solving a simple bilevel program where the lower level program is a nonconvex minimization problem with a convex set constraint. We propose to solve a combined problem where the first order condition and the value function are both present in the constraints. Since the value function is in general nonsmooth, the combined problem is in general a...

Invariant manifolds play an important role in the study of Dynamical Systems, since they help to reduce the essential dynamics o lower dimensional objects. In that way, a bifurcation analysis can easily be performed. In the classical approach, the reduction o invariant manifolds requires smoothness of the system which is typically not given for nonsmooth systems. For that reason, echniques have...

We consider the minimization of a nonsmooth convex function over a compact convex set subject to a nonsmooth convex constraint. We work in the setting of derivative-free optimization (DFO), assuming that the objective and constraint functions are available through a black-box that provides function values for lower-C2 representation of the functions. Our approach is based on a DFO adaptation of...