Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness

Convergent Semidefinite Programming Relaxations for Global Bilevel Polynomial Optimization Problems

In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming (SDP) relaxations and provide convergence results for the methods. Our scheme for problems with a ...

A New Hierarchy of Sdp-relaxations for Polynomial Programming

On Polynomial Optimization Over Non-compact Semi-algebraic Sets

We consider the class of polynomial optimization problems inf{f(x) : x ∈ K} for which the quadratic module generated by the polynomials that define K and the polynomial c − f (for some scalar c) is Archimedean. For such problems, the optimal value can be approximated as closely as desired by solving a hierarchy of semidefinite programs and the convergence is finite generically. Moreover, the Ar...

Strong duality in Lasserre's hierarchy for polynomial optimization

A polynomial optimization problem (POP) consists of minimizing a multivariate real polynomial on a semi-algebraic set K described by polynomial inequalities and equations. In its full generality it is a non-convex, multi-extremal, difficult global optimization problem. More than an decade ago, J. B. Lasserre proposed to solve POPs by a hierarchy of convex semidefinite programming (SDP) relaxati...

Equality Based Contraction of Semidefinite Programming Relaxations in Polynomial Optimization

The SDP (semidefinite programming) relaxation for general POPs (polynomial optimization problems), which was proposed as a method for computing global optimal solutions of POPs by Lasserre, has become an active research subject recently. We propose a new heuristic method exploiting the equality constraints in a given POP, and strengthen the SDP relaxation so as to achieve faster convergence to ...