Mathematical Programming: Series A and B
Testing Unconstrained Optimization Software
ACM Transactions on Mathematical Software (TOMS)
Global Optimization with Polynomials and the Problem of Moments
SIAM Journal on Optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Sparsity in sums of squares of polynomials
Mathematical Programming: Series A and B
SIAM Journal on Optimization
Semidefinite Approximations for Global Unconstrained Polynomial Optimization
SIAM Journal on Optimization
SIAM Journal on Optimization
An Extension of Sums of Squares Relaxations to Polynomial Optimization Problems Over Symmetric Cones
Mathematical Programming: Series A and B
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity
SIAM Journal on Optimization
ACM Transactions on Mathematical Software (TOMS)
A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones
Computational Optimization and Applications
Recognizing underlying sparsity in optimization
Mathematical Programming: Series A and B
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A polynomial optimization problem whose objective function is represented as a sum of positive and even powers of polynomials, called a polynomial least squares problem, is considered. Methods to transform a polynomial least square problem to polynomial semidefinite programs to reduce degrees of the polynomials are discussed. Computational efficiency of solving the original polynomial least squares problem and the transformed polynomial semidefinite programs is compared. Numerical results on selected polynomial least square problems show better computational performance of a transformed polynomial semidefinite program, especially when degrees of the polynomials are larger.