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In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…
In this paper, we solve a maximization problem where the objective function is quadratic and the constraints set is the reachable values set of a stable discrete-time affine system. This problem is equivalent to solve an infinite number of…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen…
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series…
In this article we study a broad class of integer programming problems in variable dimension. We show that these so-termed {\em n-fold integer programming problems} are polynomial time solvable. Our proof involves two heavy ingredients…
In this paper, we present an exact algorithm for optimizing two linear fractional over the efficient set of a multi-objective integer quadratic problem. This type of problems arises when two decision-makers, such as firms, each have a…
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and…
The parametric lattice-point counting problem is as follows: Given an integer matrix $A \in Z^{m \times n}$, compute an explicit formula parameterized by $b \in R^m$ that determines the number of integer points in the polyhedron $\{x \in…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
We propose a symbolic-numeric algorithm to count the number of solutions of a polynomial system within a local region. More specifically, given a zero-dimensional system $f_1=\cdots=f_n=0$, with $f_i\in\mathbb{C}[x_1,\ldots,x_n]$, and a…
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…
We obtain a polynomial-time algorithm that, given input (A, b), where A=(B|N) is an integer mxn matrix, m<n, with nonsingular mxm submatrix B and b is an m-dimensional integer vector, finds a nonnegative integer solution to the system Ax=b…
In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints,…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…