Abstract. Real-time temporal logic reasoning about trajectories of physical systems necessitates models of time which are continuous. However, discrete time temporal logic reasoning is computationally more efficient than continuous time. Moreover, in a number of engineering applications only discrete time models are available for analysis. In this paper, we introduce a framework for testing MITL specifications on continuous time signals using only discrete time analysis. The motivating idea behind our approach is that if the dynamics of the signal fulfills certain conditions and the discrete time signal robustly satisfies the MITL specification, then the corresponding continuous time signal should also satisfy the same MITL specification. 1

. The paper describes and analyzes the cost approximation algorithm. This class of iterative descent algorithms for nonlinear programs and variational inequalities places a large number of algorithms within a common framework and provides a means for analyzing relationships among seemingly unrelated methods. A common property of the methods included in the framework is that their subproblems may be characterized by monotone mappings, which replace an additive part of the original cost mapping in an iterative manner; alternately, a step is taken in the direction obtained in order to reduce the value of a merit function for the original problem. The generality of the framework is illustrated through examples, and the convergence characteristics of the algorithm are analyzed for applications to nondifferentiable optimization. The convergence results are applied to some example methods, demonstrating the strength of the analysis compared to existing results. Key Words. Nondifferentiable o...

This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are non-analytical (non-factorable), defined by a computational model for which no explicit analytical representation is available.