On tackling reverse convex constraints for non-overlapping of unequal circles

  • Chrysanthos E. Gounaris
  • Akang Wang
    • Categories Global Optimization, Global Optimization Applications Tags , , , , ,

    We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield … Read more

    Gaddum’s test for symmetric cones

  • Michael Orlitzky
    • Categories Complementarity and Variational Inequalities, Game Theory, Linear, Cone and Semidefinite Programming Tags , , , ,

    A real symmetric matrix “A” is copositive if the inner product if Ax and x is nonnegative for all x in the nonnegative orthant. Copositive programming has attracted a lot of attention since Burer showed that hard nonconvex problems can be formulated as completely-positive programs. Alas, the power of copositive programming is offset by its … Read more

    Expensive multi-objective optimization of electromagnetic mixing in a liquid metal

  • Thomas Boeck
  • Gabriele Eichfelder
  • Sebastian Prinz
  • Jörg Schumacher
  • Jana Thomann
    • Categories Mechanical Engineering, Multi-Criteria Optimization, Optimization of Simulated Systems Tags , ,

    This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet … Read more

    Active strict saddles in nonsmooth optimization

  • Damek Davis
  • Dmitriy Drusvyatskiy
    • Categories Nonsmooth Optimization Tags , , ,

    We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems. ArticleDownload View … Read more

    A subspace-accelerated split Bregman method for sparse data recovery with joint l1-type regularizers

  • Valentina De Simone
  • Daniela di Serafino
  • Marco Viola
    • Categories Convex Optimization, Finance and Economics, Nonsmooth Optimization Tags , , ,

    We propose a subspace-accelerated Bregman method for the linearly constrained minimization of functions of the form f(u)+tau_1 ||u||_1 + tau_2 ||D*u||_1, where f is a smooth convex function and D represents a linear operator, e.g. a finite difference operator, as in anisotropic Total Variation and fused-lasso regularizations. Problems of this type arise in a wide … Read more

    A Distributed Quasi-Newton Algorithm for Primal and Dual Regularized Empirical Risk Minimization

  • Stephen Wright
  • Cong Han Lim
  • Ching-pei Lee
    • Categories Nonsmooth Optimization, Parallel Algorithms Tags , , , , , , ,

    We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving empirical risk minimization (ERM) problems with a nonsmooth regularization term. Our algorithm is applicable to both the primal and the dual ERM problem. Current second-order and quasi-Newton methods for this problem either do not work well in the distributed setting or … Read more

    Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

  • Shabbir Ahmed
  • Siqian Shen
  • Beste Basciftci
    • Categories Robust Optimization, Supply Chain Management

    Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information … Read more

    Mathematical Programs with Multiobjective Generalized Nash Equilibrium Problems in the Constraints

  • L Guo
    • Categories Applications - OR and Management Sciences

    This paper considers a class of mathematical programs that include multiobjective generalized Nash equilibrium problems in the constraints. For the lower level, we deal with weakly efficient generalized Nash equilibria. Although this kind of problems has some interesting applications, there is no research focusing on it due to the difficulty resulting from its hierarchical structure … Read more

    Short simplex paths in lattice polytopes

  • Alberto Del Pia
  • Carla Michini
    • Categories Linear Programming, Polyhedra Tags , , ,

    We consider the problem of optimizing a linear function over a lattice polytope P contained in [0,k]^n and defined via m linear inequalities. We design a simplex algorithm that, given an initial vertex, reaches an optimal vertex by tracing a path along the edges of P of length at most O(n^6 k log k). The … Read more

    Finite State Approximations for Robust Markov Decision Processes

  • Kerem Ugurlu
    • Categories Applications - OR and Management Sciences

    We give a finite state approximation scheme to countable state controlled robust/risk-averse Markov chains, where there is uncertainty in the transition probability. A convergence theorem along with the corresponding rate for this approximation is established. An approximation to the stationary optimal policy is also given. Our results show a fundamental difference between the finite state … Read more