Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient ...

In this note, we provide a solution to a class of finite-horizon min–max control problems for uncertain max-plus-linear systems where the uncertain parameters are assumed to lie in a given convex and compact set, and it is required that the closed-loop input and state sequence satisfy a given set of linear inequality constraints for all admissible uncertainty realizations. We provide sufficient...

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

in this paper an approach based on evolutionary algorithms to find pareto optimal pair of state and control for multi-objective optimal control problems (moocp)'s is introduced‎. ‎in this approach‎, ‎first a discretized form of the time-control space is considered and then‎, ‎a piecewise linear control and a piecewise linear trajectory are obtained from the discretized time-control space using ...

Linear relation analysis (polyhedral analysis), devoted to discovering linear invariant relations among variables of a program, remains one of the most powerful abstract interpretations but is subject to convexity limitations. Absolute value enjoys piecewise linear expressiveness and thus natively fits to encode certain non-convex properties. Based on this insight, we propose to use linear abso...

The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints. Part I of this paper has developed a general and direct simplex algorithm for piecewise-linear programming, under convenient assumptions that guarantee a finite number of basic solutions, existence of basic feasible solutions, an...

We develop methods for rapidly identifying important components of a convex optimization problem for the purpose of achieving fast convergence times. By considering a novel problem formulation—the minimization of a sum of piecewise functions—we describe a principled and general mechanism for exploiting piecewise linear structure in convex optimization. This result leads to a theoretically justi...

We propose a fast splitting approach to the classical variational formulation of the image partitioning problem, which is frequently referred to as the Potts or piecewise constant Mumford–Shah model. For vector-valued images, our approach is significantly faster than the methods based on graph cuts and convex relaxations of the Potts model which are presently the state-of-the-art. The computati...