相关论文: Facets of a mixed-integer bilinear covering set wi…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
A quadratically constrained quadratic program (QCQP) is an optimization problem in which the objective function is a quadratic function and the feasible region is defined by quadratic constraints. Solving non-convex QCQP to global…
We identify a family of $O(|E(G)|^2)$ nontrivial facets of the connected matching polytope of a graph $G$, that is, the convex hull of incidence vectors of matchings in $G$ whose covered vertices induce a connected subgraph. Accompanying…
We show that the polyhedron defined as the convex hull of the lattice points above the hyperbola $\left\{xy = n\right\}$ has between $\Omega(n^{1/3})$ and $O(n^{1/3} \log n)$ vertices. The same bounds apply to any hyperbola with rational…
Necessary and sufficient conditions for the square-integrability of recently proposed unbiased estimators are established. A geometric characterization of a distribution that optimizes the performance of these estimators is given. An…
Computing the convex hull of a planar $n$-point set $P$ is one of the most fundamental problems in computational geometry. It has an $\Omega(n \log n)$ lower bound in the algebraic computation tree model, and many convex hull algorithms…
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer…
We analyze different ways of constructing binary extended formulations of mixed-integer problems with bounded integer variables and compare their relative strength with respect to split cuts. We show that among all binary extended…
This paper studies the convex hull of $d$-dimensional samples i.i.d. generated from spherically symmetric distributions. Specifically, we derive a complete integration formula for the expected facet number of the convex hull. This formula…
A simple method for some class of inverse obstacle scattering problems is introduced. The observation data are given by a wave field measured on a known surface surrounding unknown obstacles over a finite time interval. The wave is…
We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…
We define and study a new family of polytopes which are formed as convex hulls of partial alternating sign matrices. We determine the inequality descriptions, number of facets, and face lattices of these polytopes. We also study partial…
A planar point set is in convex position precisely when it has a convex polygonization, that is, a polygonization with maximum interior angle measure at most \pi. We can thus talk about the convexity of a set of points in terms of the…
A binarization of a bounded variable $x$ is a linear formulation with variables $x$ and additional binary variables $y_1,\dots, y_k$, so that integrality of $x$ is implied by the integrality of $y_1,\dots, y_k$. A binary extended…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with…
Mixed integer set representations, and specifically hybrid zonotopes, have enabled new techniques for reachability and verification of nonlinear and hybrid systems. Mixed-integer sets which have the property that their convex relaxation is…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…
We study the harmonic mean of non-zero complex-valued random variables (complex harmonic mean) and establish several geometric estimates and bounds. In contrast to the classical positive-valued case, complex harmonic means may lie outside…