Projected gradient methods for linearly constrained problems
Mathematical Programming: Series A and B
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Convergence of a block coordinate descent method for nondifferentiable minimization
Journal of Optimization Theory and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
SIAM Journal on Matrix Analysis and Applications
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi
ACM Transactions on Mathematical Software (TOMS)
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Multivariate Polynomial Minimization and Its Application in Signal Processing
Journal of Global Optimization
On cones of nonnegative quadratic functions
Mathematics of Operations Research
New Results on Quadratic Minimization
SIAM Journal on Optimization
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
A PTAS for the minimization of polynomials of fixed degree over the simplex
Theoretical Computer Science - Approximation and online algorithms
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity
SIAM Journal on Optimization
Analysis of iterative waterfilling algorithm for multiuser power control in digital subscriber lines
EURASIP Journal on Applied Signal Processing
Linear Equations Modulo 2 and the L1 Diameter of Convex Bodies
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Matrix Analysis and Applications
Enhanced Line Search: A Novel Method to Accelerate PARAFAC
SIAM Journal on Matrix Analysis and Applications
Z-eigenvalue methods for a global polynomial optimization problem
Mathematical Programming: Series A and B
Subdivision methods for solving polynomial equations
Journal of Symbolic Computation
GloptiPoly 3: moments, optimization and semidefinite programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
Tensor Decompositions and Applications
SIAM Review
Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Approximation algorithms for homogeneous polynomial optimization with quadratic constraints
Mathematical Programming: Series A and B - 20th International Symposium on Mathematical Programming – ISMP 2009
Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
SIAM Journal on Optimization
SIAM Journal on Optimization
New results on Hermitian matrix rank-one decomposition
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B - Special Issue on Large Scale Optimization: Analysis, Algorithms and Applications
On the best rank-1 approximation to higher-order symmetric tensors
Mathematical and Computer Modelling: An International Journal
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
Accelerated Block-coordinate Relaxation for Regularized Optimization
SIAM Journal on Optimization
A unified adaptive co-identification framework for high-d expression data
PRIB'12 Proceedings of the 7th IAPR international conference on Pattern Recognition in Bioinformatics
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In this paper we propose an efficient method for solving the spherically constrained homogeneous polynomial optimization problem. The new approach has the following three main ingredients. First, we establish a block coordinate descent type search method for nonlinear optimization, with the novelty being that we accept only a block update that achieves the maximum improvement, hence the name of our new search method: maximum block improvement (MBI). Convergence of the sequence produced by the MBI method to a stationary point is proved. Second, we establish that maximizing a homogeneous polynomial over a sphere is equivalent to its tensor relaxation problem; thus we can maximize a homogeneous polynomial function over a sphere by its tensor relaxation via the MBI approach. Third, we propose a scheme to reach a KKT point of the polynomial optimization, provided that a stationary solution for the relaxed tensor problem is available. Numerical experiments have shown that our new method works very efficiently: for a majority of the test instances that we have experimented with, the method finds the global optimal solution at a low computational cost.