Samuel Burer

On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

  • Samuel Burer
  • Karthik Natarajan
    • Categories Quadratic Programming, Robust Optimization, Semi-definite Programming Tags , ,

    We show that continuous quadratic submodular minimization with bounds is solvable in polynomial time using semidefinite programming, and we apply this result to two moment problems arising in distributionally robust optimization and the computation of covariance bounds. Accordingly, this research advances the ongoing study of continuous submodular minimization and opens new application areas therein. ArticleDownload … Read more

    An Extended Validity Domain for Constraint Learning

  • Yilin Zhu
  • Samuel Burer
    • Categories Data Science Algorithms, Optimization in Data Science Tags , , , ,

    We consider embedding a predictive machine-learning model within a prescriptive optimization problem. In this setting, called constraint learning, we study the concept of a validity domain, i.e., a constraint added to the feasible set, which keeps the optimization close to the training data, thus helping to ensure that the computed optimal solution exhibits less prediction … Read more

    A Slightly Lifted Convex Relaxation for Nonconvex Quadratic Programming with Ball Constraints

  • Samuel Burer
    • Categories Cone Programming, Global Optimization Theory, Quadratic Programming

    Globally optimizing a nonconvex quadratic over the intersection of $m$ balls in $\mathbb{R}^n$ is known to be polynomial-time solvable for fixed $m$. Moreover, when $m=1$, the standard semidefinite relaxation is exact. When $m=2$, it has been shown recently that an exact relaxation can be constructed using a disjunctive semidefinite formulation based essentially on two copies … Read more

    A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold

  • Samuel Burer
  • Kyungchan Park
    • Categories Global Optimization, Quadratic Programming, Semi-definite Programming Tags , ,

    We study semidefinite programming (SDP) relaxations for the NP-hard problem of globally optimizing a quadratic function over the Stiefel manifold. We introduce a strengthened relaxation based on two recent ideas in the literature: (i) a tailored SDP for objectives with a block-diagonal Hessian; (ii) and the use of the Kronecker matrix product to construct SDP relaxations. Using synthetic instances on … Read more

    Strengthened SDP Relaxation for an Extended Trust Region Subproblem with an Application to Optimal Power Flow

  • Samuel Burer
  • Anders Eltved
    • Categories Quadratic Programming, Semi-definite Programming Tags ,

    We study an extended trust region subproblem minimizing a nonconvex function over the hollow ball $r \le \|x\| \le R$ intersected with a full-dimensional second order cone (SOC) constraint of the form $\|x – c\| \le b^T x – a$. In particular, we present a class of valid cuts that improve existing semidefinite programming (SDP) … Read more

    Convex Hull Representations for Bounded Products of Variables

  • Kurt M. Anstreicher
  • Samuel Burer
  • Kyungchan Park
    • Categories Convex Optimization, Global Optimization Theory, Second-Order Cone Programming Tags , , ,

    It is well known that the convex hull of {(x,y,xy)}, where (x,y) is constrained to lie in a box, is given by the Reformulation-Linearization Technique (RLT) constraints. Belotti et al. (2010) and Miller et al. (2011) showed that if there are additional upper and/or lower bounds on the product z=xy, then the convex hull can … Read more

    Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic Programs

  • Samuel Burer
  • Yinyu Ye
    • Categories Global Optimization Theory, Quadratic Programming, Semi-definite Programming Tags , ,

    We study a class of quadratically constrained quadratic programs (QCQPs), called {\em diagonal QCQPs\/}, which contain no off-diagonal terms $x_j x_k$ for $j \ne k$, and we provide a sufficient condition on the problem data guaranteeing that the basic Shor semidefinite relaxation is exact. Our condition complements and refines those already present in the literature … Read more

    A Data-Driven Distributionally Robust Bound on the Expected Optimal Value of Uncertain Mixed 0-1 Linear Programming

  • Samuel Burer
  • Guanglin Xu
    • Categories Robust Optimization, Semi-definite Programming, Stochastic Programming

    This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent samples can be observed. Using the Wasserstein metric, we construct an ambiguity set centered at the empirical distribution from … Read more

    A Copositive Approach for Two-Stage Adjustable Robust Optimization with Uncertain Right-Hand Sides

  • Samuel Burer
  • Guanglin Xu
    • Categories Dynamic Programming, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , , ,

    We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which … Read more