Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
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)
Generalized normal forms and polynomial system solving
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Global optimization of rational functions: a semidefinite programming approach
Mathematical Programming: Series A and B
Sum of Squares Approximation of Polynomials, Nonnegative on a Real Algebraic Set
SIAM Journal on Optimization
SIAM Journal on Optimization
Convergent SDP-Relaxations in Polynomial Optimization with Sparsity
SIAM Journal on Optimization
A semidefinite programming approach to the generalized problem of moments
Mathematical Programming: Series A and B
Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals
Foundations of Computational Mathematics
GloptiPoly 3: moments, optimization and semidefinite programming
Optimization Methods & Software - GLOBAL OPTIMIZATION
Mathematics of Operations Research
Multivariate distributions and the moment problem
Journal of Multivariate Analysis
Minimizing ordered weighted averaging of rational functions with applications to continuous location
Computers and Operations Research
Inverse Polynomial Optimization
Mathematics of Operations Research
A Semidefinite Programming approach for solving Multiobjective Linear Programming
Journal of Global Optimization
Equilibrium problems involving the Lorentz cone
Journal of Global Optimization
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We briefly review the duality between moment problems and sums of squares (s.o.s.) representations of positive polynomials, and compare s.o.s. versus nonnegative polynomials. We then describe how to use such results to define convergent semidefinite programming relaxations in polynomial optimization as well as for the two related problems of computing the convex envelope of a rational function and finding all zeros of a system of polynomial equations.