The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization problems is known to converge finitely under some assumptions. [J.B. Lasserre. Convexity in semialgebraic geometry and polynomial optimization. SIAM J. Optim. 19, 1995-2014, 2009.] We give a new proof of the finite convergence property, that does not require the assumption that the Hessian of the objective be positive definite on the entire feasible set, but only at the optimal solution. In addition, we show that the number of steps needed for convergence depends on more than the input size of the problem. In particular, the size of the semidefinite program that gives the exact reformulation of the convex polynomial optimization problem may b...
International audienceWe consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X⊆Rn. Lasserre in...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X \subseteq \BbbR...
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization ...
We give a short introduction to Lasserre's method for minimizing a polynomial on a compact basic clo...
A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible ...
textabstractWe consider the problem of minimizing a continuous function f over a compact set (Formul...
A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a s...
The optimal value of a polynomial optimization over a compact semialgebraic set can be approximated ...
The goal of this thesis is to study a special nonlinear programming, namely, polynomial optimization...
International audienceA polynomial optimization problem (POP) consists of minimizing a multivariate ...
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hie...
We present an extension of the scalar polynomial optimization by sum-of squares de-compositions [5] ...
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequa...
This paper analyzes the relation between different orders of the Lasserre hierarchy for polynomial o...
International audienceWe consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X⊆Rn. Lasserre in...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X \subseteq \BbbR...
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization ...
We give a short introduction to Lasserre's method for minimizing a polynomial on a compact basic clo...
A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible ...
textabstractWe consider the problem of minimizing a continuous function f over a compact set (Formul...
A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a s...
The optimal value of a polynomial optimization over a compact semialgebraic set can be approximated ...
The goal of this thesis is to study a special nonlinear programming, namely, polynomial optimization...
International audienceA polynomial optimization problem (POP) consists of minimizing a multivariate ...
We consider the problem of minimizing a continuous function f over a compact set K. We analyze a hie...
We present an extension of the scalar polynomial optimization by sum-of squares de-compositions [5] ...
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequa...
This paper analyzes the relation between different orders of the Lasserre hierarchy for polynomial o...
International audienceWe consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X⊆Rn. Lasserre in...
Consider the problem of minimizing a polynomial f over a compact semialgebraic set X \subseteq \BbbR...