In this paper we will extend the input-to-state stability (ISS) framework introduced by Sontag to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for investigating non-smooth ISS Lyapunov functions is the recent focus on “multiple Lyapunov functions” for which feasible computational schemes are...

Due to the non-smoothness of Hinge loss in SVM, it is difficult obtain a faster convergence rate with modern optimization algorithms. In this paper, we introduce two smooth losses ψG(α;σ) and ψM(α;σ) which are infinitely differentiable converge uniformly α as σ tends 0. By replacing these losses, support vector machines (SSVMs), respectively. Solving SSVMs Trust Region Newton method (TRON) lead...

Time, cost and quality are considered as the main components in managing each project. Previous researches have mainly focused on the time-cost trade-off problems. Recently quality is considered as the most important factor in project�s success, which is influenced by time acceleration that is the less time is spent the more success is gained. In time-cost-quality trade-off problems, each act...

We present some algorithms for solving a number of new models of facility location which generalize the classical Fermat-Torricelli problem. Our first approach involves using the MM Principle and Nesterov’s smoothing technique to build smooth approximations that are convenient for applying smooth optimization schemes. Another approach uses subgradient-type algorithms to cope directly with the n...

In this paper, the classical economic production quantity (EPQ) model is developed for non-instantaneous deteriorating items by considering a relationship between the holding cost and the ordering cycle length. Two models are developed. First, the proposed model is considered when backorders are not permitted and this condition is waived for the second case. The cost functions associated with t...