Related papers: An algorithm for minimum cardinality generators of…
Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in ${{\mathbb R}}_+^n$. This theory is based on the observation that extremals are minimal elements…
This paper is devoted to the general problem of projection onto a polyhedral convex cone generated by a finite set of generators.This problem is reformulated into projection onto the polytope obtained by simple truncation of the original…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
Let $G$ be a finite group. In order to determine the smallest cardinality $d(G)$ of a generating set of $G$ and a generating set with this cardinality, one should repeat many times the test whether a subset of $G$ of small cardinality…
Sets of $d\times d$ matrices sharing a common invariant cone enjoy special properties, which are widely used in applications. However, finding this cone or even proving its existence/non-existence is hard. This problem is known to be…
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…
A permutomino of size n is a polyomino determined by a pair of permutations of size n+1, such that they differ in each position. In this paper, after recalling some enumerative results about permutominoes, we give a first algorithm for the…
We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle…
We construct two infinite families of algebraic minimal cones in $R^{n}$. The first family consists of minimal cubics given explicitly in terms of the Clifford systems. We show that the classes of congruent minimal cubics are in one to one…
We develop algorithms for inner approximating the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and…
It is well known that the ring of polynomial invariants of a reductive group is finitely generated. However, it is difficult to give strong upper bounds on the degrees of the generators, especially over fields of positive characteristic. In…
Although degree bounds and algorithms for the generators of various invariant rings have been known for decades, little is known about the cardinality of minimal generating sets. Estimates of such would provide lower bounds for the runtime…
The second-order cone is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a…
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
In the monotone integer dualization problem, we are given two sets of vectors in an integer box such that no vector in the first set is dominated by a vector in the second. The question is to check if the two sets of vectors cover the…
Unbiased random vectors i.e. distributed uniformly in n-dimensional space, are widely applied and the computational cost of generating a vector increases only linearly with n. On the other hand, generating uniformly distributed random…
The existence and construction of common invariant cones for families of real matrices is considered. The complete results are obtained for 2x2 matrices (with no additional restrictions) and for families of simultaneously diagonalizable…
We provide lower estimates on the minimal number of generators of the profinite completion of free products of finite groups. In particular, we show that if C_1,...,C_n are finite cyclic groups then there exists a finite group G which is…
An alternative generating function is proposed to enumerate row-convex polyominoes without internal holes on a discrete grid. The approach is based on integer partitions of the total area, where each partition corresponds to a sequence of…
We study the question whether the affine semigroup of integer points in a convex cone can be finitely generated up to symmetries of the cone. We establish general properties of finite generation up to symmetry, and then concentrate on the…