A quantitative Pólya's Theorem with corner zeros
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
On the complexity of Putinar's Positivstellensatz
Journal of Complexity
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Journal of Complexity
On the quadratic stability of descriptor systems with uncertainties in the derivative matrix
International Journal of Systems Science
Optimal SINR-based random access
INFOCOM'10 Proceedings of the 29th conference on Information communications
Partitioning procedure for polynomial optimization
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A “Joint+Marginal” Approach to Parametric Polynomial Optimization
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SIAM Journal on Optimization
Convergent SDP-relaxations for polynomial optimization with sparsity
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Computational Optimization and Applications
Minimizing ordered weighted averaging of rational functions with applications to continuous location
Computers and Operations Research
Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization
Mathematics of Operations Research
Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials
Computational Optimization and Applications
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A basic closed semialgebraic subset S of $\R^n$ is defined by simultaneous polynomial inequalities $g_1\ge 0,\dotsc,g_m\ge 0$. We give a short introduction to Lasserre's method for minimizing a polynomial f on a compact set S of this kind. It consists of successively solving tighter and tighter convex relaxations of this problem which can be formulated as semidefinite programs. We give a new short proof for the convergence of the optimal values of these relaxations to the infimum $f^\ast$ of f on S which is constructive and elementary. In the case where f possesses a unique minimizer $x^\ast$, we prove that every sequence of "nearly" optimal solutions of the successive relaxations gives rise to a sequence of points in $\R^n$ converging to $x^\ast$.