Zobrazeno 1 - 10
of 351
pro vyhledávání: '"KLEP, IGOR"'
This article studies generalizations of (matrix) convexity, including partial convexity and biconvexity, under the umbrella of $\Gamma$-convexity. Here $\Gamma$ is a tuple of free symmetric polynomials determining the geometry of a $\Gamma$-convex se
Externí odkaz:
http://arxiv.org/abs/2412.13267
In this note, we extend results about unique $n^{\textrm{th}}$ roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic
Externí odkaz:
http://arxiv.org/abs/2407.02615
This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-McCullough Positivstellensatz, the noncommutative analog of Lasserre's m
Externí odkaz:
http://arxiv.org/abs/2402.02126
A linear map $\Phi$ between matrix spaces is called cross-positive if it is positive on orthogonal pairs $(U,V)$ of positive semidefinite matrices in the sense that $\langle U,V\rangle:=\text{Tr}(UV)=0$ implies $\langle \Phi(U),V\rangle\geq0$, and is
Externí odkaz:
http://arxiv.org/abs/2401.17425
This paper studies Positivstellens\"atze and moment problems for sets $K$ that are given by universal quantifiers. Let $Q$ be a closed set and let $g = (g_1,...,g_s)$ be a tuple of polynomials in two vector variables $x$ and $y$. Then $K$ is describe
Externí odkaz:
http://arxiv.org/abs/2401.12359
We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are defined.
Externí odkaz:
http://arxiv.org/abs/2311.18707
Publikováno v:
Quantum 8, 1352 (2024)
The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between t
Externí odkaz:
http://arxiv.org/abs/2307.15661
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported on semialg
Externí odkaz:
http://arxiv.org/abs/2306.05761
Publikováno v:
SIAM J. Applied Algebra Geom. 8 (2024) 583-611
An $n\times n$ symmetric matrix $A$ is copositive if the quadratic form $x^TAx$ is nonnegative on the nonnegative orthant. The cone of copositive matrices strictly contains the cone of completely positive matrices, i.e., all matrices of the form $BB^
Externí odkaz:
http://arxiv.org/abs/2305.16224
Publikováno v:
Math. Program. 207 (2024) 645-691
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin's solution to Hilbert's 17th problem is proved showing that state polynomials, positive over all matrice
Externí odkaz:
http://arxiv.org/abs/2301.12513