Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
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Publication:607501
DOI10.1007/s10107-010-0409-zzbMath1206.90124OpenAlexW2076426934MaRDI QIDQ607501
Simai He, Zhening Li, Shu-Zhong Zhang
Publication date: 22 November 2010
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://researchportal.port.ac.uk/portal/en/publications/approximation-algorithms-for-homogeneous-polynomial-optimization-with-quadratic-constraints(66108c79-caa8-440a-a77a-3eb5714d6cec).html
Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Approximation methods and heuristics in mathematical programming (90C59)
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Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Eigenvalues and invariants of tensors
- A tensor product matrix approximation problem in quantum physics
- Jackson-type theorems in homogeneous approximation
- The complexity of optimizing over a simplex, hypercube or sphere: a short survey
- Global optimization of higher order moments in portfolio selection
- Approximating global quadratic optimization with convex quadratic constraints
- Multivariate polynomial minimization and its application in signal processing
- Semidefinite programming relaxations for semialgebraic problems
- Approximating quadratic programming with bound and quadratic constraints
- Quadratic maximization and semidefinite relaxation
- Penalized maximum-likelihood estimation, the Baum-Welch algorithm, diagonal balancing of symmetric matrices and applications to training acoustic data
- On maximization of quadratic form over intersection of ellipsoids with common center
- On the use of homogeneous polynomials to develop anisotropic yield functions with applications to sheet forming
- Eigenvalues of a real supersymmetric tensor
- A PTAS for the minimization of polynomials of fixed degree over the simplex
- Extrema of a real polynomial
- Global Optimization with Polynomials and the Problem of Moments
- Lectures on Modern Convex Optimization
- Polynomials nonnegative on a grid and discrete optimization
- On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
- A Semidefinite Relaxation Scheme for Multivariate Quartic Polynomial Optimization with Quadratic Constraints
- A Unified Theorem on SDP Rank Reduction
- GloptiPoly 3: moments, optimization and semidefinite programming
- Classical deterministic complexity of Edmonds' Problem and quantum entanglement
- Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
- Global Optimization of the Scenario Generation and Portfolio Selection Problems
- Semidefinite Relaxation Bounds for Indefinite Homogeneous Quadratic Optimization
- Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
- Semidefinite relaxation and nonconvex quadratic optimization
- SDPT3 — A Matlab software package for semidefinite programming, Version 1.3
- Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
- Multivariate Nonnegative Quadratic Mappings
- Global Minimization of Normal Quartic Polynomials Based on Global Descent Directions
- An Eigenvalue Method for Testing Positive Definiteness of a Multivariate Form
- Blind constant modulus equalization via convex optimization
- Approximation Bounds for Quadratic Optimization with Homogeneous Quadratic Constraints
- GloptiPoly
- Complex Quadratic Optimization and Semidefinite Programming
- Approximation by homogeneous polynomials