Lasserre’s hierarchy

Strengthening Lasserre’s Hierarchy in Real and Complex Polynomial Optimization

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

    We establish a connection between multiplication operators and shift operators. Moreover, we derive positive semidefinite conditions of finite rank moment sequences and use these conditions to strengthen Lasserre’s hierarchy for real and complex polynomial optimization. Integration of the strengthening technique with sparsity is considered. Extensive numerical experiments show that our strengthening technique can significantly improve … 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