Related papers: New special cases of the Quadratic Assignment Prob…
The Quadratic Assignment Problem, QAP, is a classic combinatorial optimization problem, classified as NP-hard and widely studied. This problem consists in assigning N facilities to N locations obeying the relation of 1 to 1, aiming to…
In this paper we introduce a new parameterized Quadratic Decision Rule (QDR), a generalisation of the commonly employed Affine Decision Rule (ADR), for two-stage linear adjustable robust optimization problems with ellipsoidal uncertainty…
Solving point-wise feature correspondence in visual data is a fundamental problem in computer vision. A powerful model that addresses this challenge is to formulate it as graph matching, which entails solving a Quadratic Assignment Problem…
We study the set of optimal solutions of the dual linear programming formulation of the linear assignment problem (LAP) to propose a method for computing a solution from the relative interior of this set. Assuming that an arbitrary…
This paper continues research initiated in quant-ph/0201022 . The main subject here is the so-called Edmonds' problem of deciding if a given linear subspace of square matrices contains a nonsingular matrix . We present a deterministic…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems…
We investigate a special case of the maximum quadratic assignment problem where one matrix is a product matrix and the other matrix is the distance matrix of a one-dimensional point set. We show that this special case, which we call the…
For any optimisation problem where diverse algorithmic approaches are available, the task of predicting algorithm performance and selecting the algorithm most likely to perform well on a given instance holds great practical interest.…
We provide a solution to the problem of simultaneous $diagonalization$ $via$ $congruence$ of a given set of $m$ complex symmetric $n\times n$ matrices $\{A_{1},\ldots,A_{m}\}$, by showing that it can be reduced to a possibly…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
Matrix polynomials with unitary/doubly stochastic coefficients form the subject matter of this manuscript. We prove that if $P(\lambda)$ is a quadratic matrix polynomial whose coefficients are either unitary matrices or doubly stochastic…
We consider the bipartite boolean quadric polytope (BQP) with multiple-choice constraints and analyse its combinatorial properties. The well-studied BQP is defined as the convex hull of all quadric incidence vectors over a bipartite graph.…
We consider two polytopes. The quadratic assignment polytope $QAP(n)$ is the convex hull of the set of tensors $x\otimes x$, $x \in P_n$, where $P_n$ is the set of $n\times n$ permutation matrices. The second polytope is defined as follows.…
In the theory of matrix-valued orthogonal polynomials, there exists a longstanding problem known as the Matrix Bochner Problem: the classification of all $N \times N$ weight matrices $W(x)$ such that the associated orthogonal polynomials…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…
We introduce a new strategy in solving the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment}…
It is known that difference equations generated as the Newton-Raphson iteration for quadratic equations are solvable in closed form, and the solution can be constructed from linear three-term recurrence relations with constant coefficients.…