相关论文: Polynomial hulls and an optimization problem

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ random points in $K$ independently according to the uniform distribution. The convex hull of these points, denoted by $K_n$, is called a {\it random polytope}. We prove…

Given a convex set and an interior point close to the boundary, we prove the existence of a supporting hyperplane whose distance to the point is controlled, in a dimensionally quantified way, by the thickness of the convex set in the…

We describe an algorithm computing the monodromy and the pole order filtration on the Milnor fiber cohomology of any reduced projective plane curve $C$. The relation to the zero set of Bernstein-Sato polynomial of the defining homogeneous…

Suppose that the set ${\mathcal{T}}= \{T_1, T_2,...,T_q \} $ of real $n\times n$ matrices has joint spectral radius less than $1$. Then for any digit set $ D= \{d_1, \cdots, d_q\} \subset {\Bbb R}^n$, there exists a unique nonempty compact…

We consider bounded integer knapsacks where the weights and variable upper bounds together form a superincreasing sequence. The elements of this superincreasing knapsack are exactly those vectors that are lexicographically smaller than the…

In this paper we focus on the tropical convex hull of convex sets and polyhedral complexes. We give a vertex description of the tropical convex hull of a line segment and a ray. %in \RR^{n+1}/\RR\mathbf{1}. Next we show that tropical convex…

In this note we investigate the behavior of the volume that the convex hull of two congruent and intersecting simplices in Euclidean $n$-space can have. We prove some useful equalities and inequalities on this volume. For the regular…

Given a polynomial $x \in {\mathbb R}^n \mapsto p(x)$ in $n=2$ variables, a symbolic-numerical algorithm is first described for detecting whether the connected component of the plane sublevel set ${\mathcal P} = \{x : p(x) \geq 0\}$…

We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…

Motivated by previous efforts toward mathematically analyzing the treatment of monomials in spatial branch-and-bound, we study the convex hull of the graph of a simple monomial on a nonnegative box domain in arbitrary dimension, where at…

This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…

It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…

Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the closed convex hulls of joint unitary orbits are completely…

In this work, we introduce and study the forbidden-vertices problem. Given a polytope P and a subset X of its vertices, we study the complexity of linear optimization over the subset of vertices of P that are not contained in X. This…

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the…

We formalise decompression planning as an optimal control problem with gas feasibility windows (ppO$_2$, END), affine ceilings, and convex penalties in normalised oversaturation. The depth trajectory is constrained to be a monotone ascent,…

Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…

We discuss connections between certain well-known open problems related to the uniform measure on a high-dimensional convex body. In particular, we show that the "thin shell conjecture" implies the "hyperplane conjecture". This extends a…

We describe convex hulls of the simplest compact space curves, reducible quartics consisting of two circles. When the circles do not meet in complex projective space, their algebraic boundary contains an irrational ruled surface of degree…