We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa the value of a parameter that results in the smallest magnitude of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control systems. Many systems require the spectra to lie in the left half plane in order for stability ...

In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

A novel class of variational models with nonconvex lq-normtype regularizations (0 < q < 1) is considered, which typically outperforms those models with convex regularizations in restoring sparse images. Due to the fact that the objective function is nonconvex and non-Lipschitz, such nonconvex models are very challenging from an analytical as well as numerical point of view. In this work we prop...

We propose a single time-scale stochastic subgradient method for constrained optimization of composition several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz differentiable in generalized sense. Only estimates the values derivatives used. is parameter-free. prove convergence with probability one method, by associating it system differential inclusions dev...

Given a weakly uniformly globally asymptotically stable closed (not necessarily compact) set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability to a closed (not necessarily compact)...

In this note we consider the computability of the solution of the initial-value problem for ordinary differential equations with continuous right-hand side. We present algorithms for the computation of the solution using the “thousand monkeys” approach, in which we generate all possible solution tubes, and then check which are valid. In this way, we show that the solution of a differential equa...

Abstract In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential condition on portion described by Clarke generalized gradient locally Lipschitz function. First, prove new existence result for inequality employing theory pseudomonotone operators. Next, give comparis...

In this paper we consider the computability of the solution of the initialvalue problem for differential inclusions with semicontinuous right-hand side. We present algorithms for the computation of the solution using the “ten thousand monkeys” approach, in which we generate all possible solution tubes, and then check which are valid. In this way, we show that the solution of an upper-semicontin...