We study the minimum number of constraints needed to formulate random instances of the maximum stable set problem via LPs (more precisely, linear extended formulations), in two distinct models. In the uniform model, the constraints of the LP are not allowed to depend on the input graph, which should be encoded solely in the objective function. There we prove a 2Ω(n/ log n) lower bound with prob...

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...

Abstract: In this paper, the stabilization problem of discrete-time bilinear systems by linear state-feedback control is investigated. First, conditions guaranteeing the positive invariance of polyhedral sets with respect to nonlinear systems with second order polynomial nonlinearity are established. Then these results are used for the determination of linear state-feedback unconstrained and co...

In this paper the concept of set invariance for time-delay systems is introduced with a specific attention to the linear discrete-time case. We are interested in the definition of a D(elay)invariant set with respect to a bounded polyhedral subset of the state-space. D-invariance conditions are derived based on the Minkowski addition in a first stage, and subsequently translated in feasibility-b...

We propose a hull operator, the reflex-free hull, that allows us to define a 3D analogue to bays in polygons. The reflex-free hull allows a rich set of topological types, yet for polyhedral input with n edges, it remains a polyhedral set with O(n) edges. This is in contrast to other possible hull definitions that give non-planar surfaces and higher combinatorial complexity. The reflex-free hull...

This paper extends the Log-robust portfolio management approach to the case with short sales, i.e., the case where the manager can sell shares he does not yet own. We model the continuously compounded rates of return, which have been established in the literature as the true drivers of uncertainty, as uncertain parameters belonging to polyhedral uncertainty sets, and maximize the worst-case por...

We consider the volumetric barrier for semide2nite programming, or “generalized” volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semide2nite case. Our analysis facilitates a simpli2ed proof of self-concordance for the semide2nite volumetric barrier, as well as for the combined volumetri...

This paper presents a new context-free parsing algorithm based on a bidirectional strictly horizontal strategy which incorporates strong top–down predictions (derivations and adjacencies). From a functional point of view, the parser is able to propagate syntactic constraints reducing parsing ambiguity. From a computational perspective, the algorithm includes different techniques aimed at the im...

We consider the volumetric barrier for semideenite programming, or \generalized" volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semideenite case. Our analysis facilitates a simpliied proof of self-concordancy for the semideenite volu-metric barrier, as well as for the combined volumetr...

We study infinite dimensional optimization problems where the constraint mapping is given as the sum of a smooth function and a generalized polyhedral multifunction, e.g. the normal cone mapping of a convex polyhedral set. By using advanced techniques of variational analysis we obtain first-order and second-order characterizations, both necessary and sufficient, for directional metric subregula...