Ahmadreza Marandi

Solving sparse polynomial optimization problems with chordal structure using the sparse, bounded-degree sum-of-squares hierarchy

  • Joachim Dahl
  • Etienne de Klerk
  • Ahmadreza Marandi
    • Categories Global Optimization, Quadratic Programming, Semi-definite Programming Tags , , , ,

    The sparse bounded degree sum-of-squares (sparse-BSOS) hierarchy of Weisser, Lasserre and Toh [arXiv:1607.01151,2016] constructs a sequence of lower bounds for a sparse polynomial optimization problem. Under some assumptions, it is proven by the authors that the sequence converges to the optimal value. In this paper, we modify the hierarchy to deal with problems containing equality … Read more

    A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem

  • Joachim Dahl
  • Etienne de Klerk
  • Ahmadreza Marandi
    • Categories Nonlinear Optimization, Semi-definite Programming Tags , , ,

    The bounded degree sum-of-squares (BSOS) hierarchy of Lasserre, Toh, and Yang [EURO J. Comput. Optim., 2015] constructs lower bounds for a general polynomial optimization problem with compact feasible set, by solving a sequence of semi-definite programming (SDP) problems. Lasserre, Toh, and Yang prove that these lower bounds converge to the optimal value of the original … Read more

    When are static and adjustable robust optimization with constraint-wise uncertainty equivalent?

  • Dick den Hertog
  • Ahmadreza Marandi
    • Categories Robust Optimization Tags , , ,

    Adjustable Robust Optimization (ARO) yields, in general, better worst-case solutions than static Robust Optimization (RO). However, ARO is computationally more difficult than RO. In this paper, we derive conditions under which the worst-case objective values of ARO and RO problems are equal. We prove that if the uncertainty is constraint-wise and the adjustable variables lie … Read more