In this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polygons, i.e., polygons that are locally convex, except possibly at the vertices, and their edges are convex arcs. We transform the problem of monitoring a piecewise-convex polygon to the problem of 2dominat...

This paper describes an approach to reformulating the stereo matching problem as a large scale Linear Program. The approach proceeds by approximating the match cost function associated with each pixel with a piecewise linear convex function. Regularization terms related to the first and second derivative of the disparity field are also captured with piecewise linear penalty terms. The resulting...

This paper addresses Markov Decision Processes over compact state and action spaces. We investigate the special case of linear dynamics and piecewise-linear and convex immediate costs for the average cost criterion. This model is very general and covers many interesting examples, for instance in inventory management. Due to the curse of dimensionality, the problem is intractable and optimal pol...

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semi-definite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex ...

This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear appro...

Abstract. The main goal of the paper is to establish that the L1 norm of jumps of the normal derivative across element boundaries and the L1 norm of the Laplacian of a piecewise polynomial finite element function can be controlled by corresponding weighted discrete H2 norm on convex polyhedral domains. In the finite element literature such results are only available for piecewise linear element...

This paper introduces the dual parameter set of a piecewise affine (PWA) system. This is a key concept to enable a convex formulation of PWA controller synthesis for PWA slab differential inclusions using a new convex relaxation. Another important contribution of the paper is to present PWA L2-gain analysis and synthesis results for PWA systems whose output is also a PWA function of the state (...