Certifying optimality of Bell inequality violations: noncommutative polynomial optimization through semidefinite programming and local optimization
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Publication:6490315
DOI10.1137/22M1473340MaRDI QIDQ6490315
Timotej Hrga, Janez Povh, Igor Klep
Publication date: 23 April 2024
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Gröbner basiseigenvalue optimizationsemidefinite programmingGNS constructionnoncommutative polynomialBell inequalityviolationArtin-Wedderburn theory
Semidefinite programming (90C22) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10) Real algebra (13J30)
Cites Work
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- Conic optimization via operator splitting and homogeneous self-dual embedding
- Optimality conditions and finite convergence of Lasserre's hierarchy
- SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints
- A numerical algorithm for block-diagonal decomposition of matrix \(*\)-algebras with application to semidefinite programming
- A boundary point method to solve semidefinite programs
- On the limited memory BFGS method for large scale optimization
- Computing a nearest symmetric positive semidefinite matrix
- Extremal psd forms with few terms
- Multiplicative bases, Gröbner bases, and right Gröbner bases
- Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization
- ``Positive noncommutative polynomials are sums of squares.
- Unbounded induced representations of \(\ast \)-algebras
- Sparse noncommutative polynomial optimization
- \texttt{MADAM}: a parallel exact solver for max-cut based on semidefinite programming and ADMM
- Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
- Global Optimization with Polynomials and the Problem of Moments
- Optimization of Polynomials in Non-Commuting Variables
- TSIRELSON'S PROBLEM AND KIRCHBERG'S CONJECTURE
- Constrained Polynomial Optimization Problems with Noncommuting Variables
- A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
- Convergent Relaxations of Polynomial Optimization Problems with Noncommuting Variables
- NCSOStools: a computer algebra system for symbolic and numerical computation with noncommutative polynomials
- BiqCrunch
- Quantum Bilinear Optimization
- GloptiPoly 3: moments, optimization and semidefinite programming
- Semidefinite Approximations of Projections and Polynomial Images of SemiAlgebraic Sets
- Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization
- Bell Inequalities: Many Questions, a Few Answers
- Flat extensions of positive moment matrices: recursively generated relations
- Minimizer Extraction in Polynomial Optimization Is Robust
- A positivstellensatz for non-commutative polynomials
- Semidefinite Optimization and Convex Algebraic Geometry
- The truncated complex $K$-moment problem
- Sparse Polynomial Optimization
- Chordal-TSSOS: A Moment-SOS Hierarchy That Exploits Term Sparsity with Chordal Extension
- Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
- Connes' embedding problem and Tsirelson's problem
- Optimization of Polynomials on Compact Semialgebraic Sets
- Proposed Experiment to Test Local Hidden-Variable Theories
- DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
- Two-party Bell inequalities derived from combinatorics via triangular elimination
- MIP* = RE
- Factorization of operator-valued polynomials in several non-commuting variables
- Solving SDP relaxations of max-cut problem with large number of hypermetric inequalities by L-BFGS-B
- Noncommutative nullstellensätze and perfect games
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