Optimization of Polynomial Fractional Functions
Journal of Global Optimization
A linear programming reformulation of the standard quadratic optimization problem
Journal of Global Optimization
An alternative approach for non-linear optimal control problems based on the method of moments
Computational Optimization and Applications
Global optimization for sum of generalized fractional functions
Journal of Computational and Applied Mathematics
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
SIAM Journal on Optimization
Exploiting equalities in polynomial programming
Operations Research Letters
Computational Optimization and Applications
Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications
Journal of Global Optimization
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We consider the global minimization of a multivariate polynomial on a semi-algebraic set O defined with polynomial inequalities. We then compare two hierarchies of relaxations, namely, LP relaxations based on products of the original constraints, in the spirit of the RLT procedure of Sherali and Adams (1990), and recent semidefinite programming (SDP) relaxations introduced by the author. The comparison is analyzed in light of recent results in real algebraic geometry on various representations of polynomials, positive on a compact semi-algebraic set.