Lasserre’s hierarchy

A Bilevel Hierarchy of Strengthened Complex Moment Relaxations for Complex Polynomial Optimization

  • Jie Wang
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Semi-definite Programming Tags , , ,

    This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the normality of the so-called shift operators. The relaxation problem in this new hierarchy is parameterized by the usual relaxation order as well as … Read more

    Certifying Global Optimality of AC-OPF Solutions via sparse polynomial optimization

  • Jie Wang
  • Victor Magron
  • Jean-Bernard Lasserre
    • Categories Global Optimization Applications, Semi-definite Programming Tags , , , , ,

    We report the experimental results on certifying 1% global optimality of solutions of AC-OPF instances from PGLiB via the CS-TSSOS hierarchy — a moment-SOS based hierarchy that exploits both correlative and term sparsity, which can provide tighter SDP relaxations than Shor’s relaxation. Our numerical experiments demonstrate that the CS-TSSOS hierarchy scales well with the problem … Read more