Convergent relaxations of polynomial optimization problems with noncommuting variables
We consider optimization problems with polynomial inequality constraints in noncommuting
variables. These noncommuting variables are viewed as bounded operators on a Hilbert …
variables. These noncommuting variables are viewed as bounded operators on a Hilbert …
Sparse noncommutative polynomial optimization
This article focuses on optimization of polynomials in noncommuting variables, while taking
into account sparsity in the input data. A converging hierarchy of semidefinite relaxations for …
into account sparsity in the input data. A converging hierarchy of semidefinite relaxations for …
Algorithm 950: Ncpol2sdpa—sparse semidefinite programming relaxations for polynomial optimization problems of noncommuting variables
P Wittek - ACM Transactions on Mathematical Software (TOMS), 2015 - dl.acm.org
A hierarchy of semidefinite programming (SDP) relaxations approximates the global
optimum of polynomial optimization problems of noncommuting variables. Generating the …
optimum of polynomial optimization problems of noncommuting variables. Generating the …
[图书][B] Optimization of polynomials in non-commuting variables
Optimization problems involving polynomial data arise across many sciences, eg, in control
theory [Che10, HG05, Sch06], operations research [Sho90, Nie09], statistics and probability …
theory [Che10, HG05, Sch06], operations research [Sho90, Nie09], statistics and probability …
Toward a noncommutative arithmetic-geometric mean inequality: Conjectures, case-studies, and consequences
Randomized algorithms that base iteration-level decisions on samples from some pool are
ubiquitous in machine learning and optimization. Examples include stochastic gradient …
ubiquitous in machine learning and optimization. Examples include stochastic gradient …
[HTML][HTML] The convex Positivstellensatz in a free algebra
JW Helton, I Klep, S McCullough - Advances in Mathematics, 2012 - Elsevier
Given a monic linear pencil L in g variables, let [Formula: see text] where and Sng is the set
of g-tuples of symmetric n× n matrices. Because L is a monic linear pencil, each PL (n) is …
of g-tuples of symmetric n× n matrices. Because L is a monic linear pencil, each PL (n) is …
Optimization over trace polynomials
Motivated by recent progress in quantum information theory, this article aims at optimizing
trace polynomials, ie, polynomials in noncommuting variables and traces of their products. A …
trace polynomials, ie, polynomials in noncommuting variables and traces of their products. A …
Beneath the valley of the noncommutative arithmetic-geometric mean inequality: conjectures, case-studies, and consequences
Randomized algorithms that base iteration-level decisions on samples from some pool are
ubiquitous in machine learning and optimization. Examples include stochastic gradient …
ubiquitous in machine learning and optimization. Examples include stochastic gradient …
Chapter 8: Free Convex Algebraic Geometry
JW Helton, I Klep, S McCullough - Semidefinite optimization and convex …, 2012 - SIAM
A new development is extension of the algebraic certificates of real algebraic geometry to
noncommutative polynomials, thereby giving a theory of noncommutative polynomial …
noncommutative polynomials, thereby giving a theory of noncommutative polynomial …
The tracial moment problem and trace-optimization of polynomials
The main topic addressed in this paper is trace-optimization of polynomials in
noncommuting (nc) variables: given an nc polynomial f, what is the smallest trace f (A) can …
noncommuting (nc) variables: given an nc polynomial f, what is the smallest trace f (A) can …