Related papers: A certificate for semidefinite relaxations in comp…
For a degree 2n real d-dimensional multisequence \beta^(2n) to have a representing measure, it is necessary for the associated moment matrix M(n) to be positive semidefinite and for the algebraic variety V = V(\beta) associated to \beta to…
Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In…
The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
This paper is concerned with the calmness of a partial perturbation to the composite rank constraint system, an intersection of the rank constraint set and a general closed set, which is shown to be equivalent to a local Lipschitz-type…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
We present a technique for reducing the computational requirements by several orders of magnitude in the evaluation of semidefinite relaxations for bounding the set of quantum correlations arising from finite-dimensional Hilbert spaces. The…
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance. The first class of problem…
A real symmetric n times n matrix is called copositive if the corresponding quadratic form is non-negative on the closed first orthant. If the matrix fails to be copositive there exists some non-negative certificate for which the quadratic…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
Relying on the co-area formula, an exact relaxation framework for minimizing objectives involving the total variation of a binary valued function (of bounded variation) is presented. The underlying problem class covers many important…
This paper proposes tight semidefinite relaxations for polynomial optimization. The optimality conditions are investigated. We show that generally Lagrange multipliers can be expressed as polynomial functions in decision variables over the…
To compute difference Groebner bases of ideals generated by linear polynomials we adopt to difference polynomial rings the involutive algorithm based on Janet-like division. The algorithm has been implemented in Maple in the form of the…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
We review several (and provide new) results on the theory of moments, sums of squares and basic semi-algebraic sets when convexity is present. In particular, we show that under convexity, the hierarchy of semidefinite relaxations for…
Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$…
A new symbolic algorithm to compute sums of squares multipliers (certificates) to witness the membership of non-negative univariate polynomials in a saturated univariate quadratic module is presented. Certificates are first computed in…
A Comprehensive Grobner system for a parametric ideal I in K(A)[X] represents the collection of all Grobner bases of the ideals I' in K[X] obtained as the values of the parameters A vary in K. The recent algorithms for computing them…
Let M be an archimedean quadratic module of real t-by-t matrix polynomials in n variables, and let S be the set of all real n-tuples where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of…