Related papers: Solving Tantrix via Integer Programming
The main contribution of this thesis is the development of a new algorithm for solving convex quadratic programs. It consists in combining the method of multipliers with an infeasible active-set method. Our approach is iterative. In each…
In a broad sense, artificial intelligence is a service to find a solution to complex intellectual problems. In this sense, the MathPartner service provides artificial intelligence that allows us to formulate questions and receive answers to…
Chaotic attractors are solutions of deterministic processes, of which the topology can be described by templates. We consider templates of chaotic attractors bounded by a genus-1 torus described by a linking matrix. This article introduces…
We introduce a Three Tier Tree Calculus (3TC) that defines in a systematic way three tiers of tree structures underlying proof search in logic programming. We use 3TC to define a new -- structural -- version of resolution for logic…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
We wish to tile a rectangle or a torus with only vertical and horizontal bars of a given length, such that the number of bars in every column and row equals given numbers. We present results for particular instances and for a more general…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
Formally verifying properties of programs that manipulate arrays in loops is computationally challenging. In this paper, we focus on a useful class of such programs, and present a novel property-driven verification method that first infers…
Optimization problems are considered in the framework of tropical algebra to minimize and maximize a nonlinear objective function defined on vectors over an idempotent semifield, and calculated using multiplicative conjugate transposition.…
We present experimental and theoretical results on a method that applies a numerical solver iteratively to solve several non-negative quadratic programming problems in geometric optimization. The method gains efficiency by exploiting the…
Program synthesis aims to automatically construct human-readable programs that satisfy given task specifications, such as input/output pairs or demonstrations. Recent works have demonstrated encouraging results in a variety of domains, such…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by…
Solving integer programs of the form $\min \{\mathbf{x} \mid A\mathbf{x} = \mathbf{b}, \mathbf{l} \leq \mathbf{x} \leq \mathbf{u}, \mathbf{x} \in \mathbb{Z}^n \}$ is, in general, $\mathsf{NP}$-hard. Hence, great effort has been put into…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of…
Timetabling is a typical application of constraint programming whose task is to allocate activities to slots in available resources respecting various constraints like precedence and capacity. In this paper we present a basic concept, a…
In this paper we introduce an evolutionary algorithm for the solution of linear integer programs. The strategy is based on the separation of the variables into the integer subset and the continuous subset; the integer variables are fixed by…
We propose iterative projection methods for solving square or rectangular consistent linear systems Ax = b. Existing projection methods use sketching matrices (possibly randomized) to generate a sequence of small projected subproblems, but…
In 2022, Olivier Longuet, a French mathematics teacher, created a game called the \textit{calissons puzzle}. Given a triangular grid in a hexagon and some given edges of the grid, the problem is to find a calisson tiling such that no input…