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In this paper, we study the mixed-integer nonlinear set given by a separable quadratic constraint on continuous variables, where each continuous variable is controlled by an additional indicator. This set occurs pervasively in optimization…
This paper provides full \Matlab-code and informal correctness proofs for the lexicographic reverse search algorithm for convex hull calculations. The implementation was tested on a 1993 486-PC for various small and some larger, partially…
We describe the implementation of a subfield of the field of formal Puiseux series in polymake. This is employed for solving linear programs and computing convex hulls depending on a real parameter. Moreover, this approach is also useful…
In this paper we present several results on the expected complexity of a convex hull of $n$ points chosen uniformly and independently from a convex shape. (i) We show that the expected number of vertices of the convex hull of $n$ points,…
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 consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…
Given a directed graph D = (N, A) and a sequence of positive integers 1 <= c_1 < c_2 < ... < c_m <= |N|, we consider those path and cycle polytopes that are defined as the convex hulls of simple paths and cycles of D of cardinality c_p for…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
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…
The resolution of linear system with positive integer variables is a basic yet difficult computational problem with many applications. We consider sparse uncorrelated random systems parametrised by the density $c$ and the ratio $\alpha=N/M$…
We derive a linear programming bound on the maximum cardinality of error-correcting codes in the sum-rank metric. Based on computational experiments on relatively small instances, we observe that the obtained bounds outperform all…
For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
In this paper, we explore the challenge of assortment planning in the context of quick-commerce, a rapidly-growing business model that aims to deliver time-sensitive products. In order to achieve quick delivery to satisfy the immediate…
This paper concerns the number of lattice points in the plane which are visible along certain curves to all elements in some set S of lattice points simultaneously. By proposing the concept of level of visibility, we are able to analyze…
We prove tight upper bounds for the number of vertices of a simple polygon that is the union or the intersection of two simple polygons with given numbers of convex and concave vertices. The similar question on graphs of the lower (or…
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when…