Sum-of-squares hierarchies for polynomial optimization and the Christoffel--Darboux kernel
L Slot - SIAM Journal on Optimization, 2022 - SIAM
Consider the problem of minimizing a polynomial f over a compact semialgebraic set
X⊆R^n. Lasserre introduces hierarchies of semidefinite programs to approximate this hard …
X⊆R^n. Lasserre introduces hierarchies of semidefinite programs to approximate this hard …
Sum-of-squares hierarchies for binary polynomial optimization
We consider the sum-of-squares hierarchy of approximations for the problem of minimizing a
polynomial f over the boolean hypercube B^ n={0, 1\}^ n B n= 0, 1 n. This hierarchy provides …
polynomial f over the boolean hypercube B^ n={0, 1\}^ n B n= 0, 1 n. This hierarchy provides …
Relaxations for binary polynomial optimization via signed certificates
We consider the problem of minimizing a polynomial $ f $ over the binary hypercube. We
show that, for a specific set of polynomials, their binary non-negativity can be checked in a …
show that, for a specific set of polynomials, their binary non-negativity can be checked in a …
Tight Sum-of-Squares lower bounds for binary polynomial optimization problems
For binary polynomial optimization problems of degree 2d with n variables Sakaue, Takeda,
Kim, and Ito proved that the th semidefinite (SDP) relaxation in the SoS/Lasserre hierarchy of …
Kim, and Ito proved that the th semidefinite (SDP) relaxation in the SoS/Lasserre hierarchy of …
Tight sum-of-squares lower bounds for binary polynomial optimization problems
We give two results concerning the power of the Sum-of-Squares (SoS)/Lasserre hierarchy.
For binary polynomial optimization problems of degree $2 d $ and an odd number of …
For binary polynomial optimization problems of degree $2 d $ and an odd number of …
Asymptotic analysis of semidefinite bounds for polynomial optimization and independent sets in geometric hypergraphs
L Slot - 2022 - research.tilburguniversity.edu
The goal of a mathematical optimization problem is to maximize an objective (or minimize a
cost) under a given set of rules, called constraints. Optimization has many applications, both …
cost) under a given set of rules, called constraints. Optimization has many applications, both …
Binary quadratic optimization problems that are difficult to solve by conic relaxations
S Kim, M Kojima - Discrete Optimization, 2017 - Elsevier
We study conic relaxations including semidefinite programming (SDP) relaxations and
doubly nonnegative programming (DNN) relaxations to find the optimal values of binary …
doubly nonnegative programming (DNN) relaxations to find the optimal values of binary …
Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time
The problem of verifying the nonnegativity of a function on a finite abelian group is a long-
standing challenging problem. The basic representation theory of finite groups indicates that …
standing challenging problem. The basic representation theory of finite groups indicates that …
SoS certification for symmetric quadratic functions and its connection to constrained Boolean hypercube optimization
We study the rank of the Sum of Squares (SoS) hierarchy over the Boolean hypercube for
Symmetric Quadratic Functions (SQFs) in $ n $ variables with roots placed in points $ k-1 …
Symmetric Quadratic Functions (SQFs) in $ n $ variables with roots placed in points $ k-1 …
An Effective Positivstellensatz over the Rational Numbers for Finite Semialgebraic Sets
We study the problem of representing multivariate polynomials with rational coefficients,
which are nonnegative and strictly positive on finite semialgebraic sets, using rational sums …
which are nonnegative and strictly positive on finite semialgebraic sets, using rational sums …