Local superlinear convergence of polynimial-time interior-point methods for hyperbolicity cone optimization problems;
This paper addresses the tolerance approach to the sensitivity analysis of optimal solutions to a nonlinear optimization problem of the form: minimize the total cost of a trajectory over all admissible discrete trajectories, where the total cost is expressed through individual costs by means of a generalized addition operation on the set of all non-negative or positive reals. We evaluate and present sharp estimates for upper and lower bounds of costs, for which an optimal solution to the above problem remains stable. These bounds present new results in the sensitivity analysis, as well as extend in a unified way most known results. We define an invariant of the optimization problem—the tolerance function, which is independent of optimal solutions, and establish its basic properties, among which are a characterization of the set of all optimal solutions, the uniqueness of an optimal solution, and extremal values of the tolerance function on an optimal solution.
The policy of maintenance support of a complicated engineering system, providing the maximum effectiveness of its service, is considered. The solved optimization problem of integer programming allows combining the structural elements of a project into groups, optimal from the position of minimization of inter-group connections.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.