Month: September 2016

Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

  • Ruiwei Jiang
  • Siqian Shen
  • Yiling Zhang
    • Categories 0-1 Programming, Second-Order Cone Programming, Stochastic Programming

    We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more

    Nonsmooth optimization using Taylor-like models: error bounds, convergence, and termination criteria

  • Dmitriy Drusvyatskiy
  • Adrian Lewis
  • Alexander D. Ioffe
    • Categories Nonsmooth Optimization Tags , , , ,

    We consider optimization algorithms that successively minimize simple Taylor-like models of the objective function. Methods of Gauss-Newton type for minimizing the composition of a convex function and a smooth map are common examples. Our main result is an explicit relationship between the step-size of any such algorithm and the slope of the function at a … Read more

    A New First-order Algorithmic Framework for Optimization Problems with Orthogonality Constraints

  • Xiaojun Chen
  • Bin Gao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization Tags , , , , ,

    In this paper, we consider a class of optimization problems with orthogonality constraints, the feasible region of which is called the Stiefel manifold. Our new framework combines a function value reduction step with a correction step. Different from the existing approaches, the function value reduction step of our algorithmic framework searches along the standard Euclidean … Read more

    Open research areas in distance geometry

  • Carlile Lavor
  • Leo Liberti
    • Categories Basic Sciences Applications, Data-Mining, Global Optimization Applications Tags , , , ,

    Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open and promising research areas. Article Download View Open research areas in distance geometry

    Adjustable robust strategies for flood protection

  • Dick den Hertog
  • Krzysztof Postek
  • Jarl Kind
  • Chris Pustjens
    • Categories Civil and Environmental Engineering Tags , , ,

    Flood protection is of major importance to many flood-prone regions and involves substantial investment and maintenance costs. Modern flood risk management requires often to determine a cost-efficient protection strategy, i.e., one with lowest possible long run cost and satisfying flood protection standards imposed by the regulator throughout the entire planning horizon. There are two challenges … Read more

    Efficient methods for several classes of ambiguous stochastic programming problems under mean-MAD information

  • Dick den Hertog
  • Krzysztof Postek
  • Ward Romeijnders
  • Maarten H. van der Vlerk
    • Categories Robust Optimization, Stochastic Programming

    We consider decision making problems under uncertainty, assuming that only partial distributional information is available – as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be … Read more

    Mixed Integer Quadratic Optimization Formulations for Eliminating Multicollinearity Based on Variance Inflation Factor

  • Ken Kobayashi
  • Tomomi Matsui
  • Ryuhei Miyashiro
  • Kazuhide Nakata
  • Yuichi Takano
  • Ryuta Tamura
    • Categories Applications - Science and Engineering, Integer Programming, Statistics Tags , , , , ,

    The variance inflation factor, VIF, is the most frequently used indicator for detecting multicollinearity in multiple linear regression models. This paper proposes two mixed integer quadratic optimization formulations for selecting the best subset of explanatory variables under upper-bound constraints on VIF of selected variables. Computational results illustrate the effectiveness of our optimization formulations based on … Read more

    Time and Dynamic Consistency of Risk Averse Stochastic Programs

  • Alois Pichler
  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , ,

    In various settings time consistency in dynamic programming has been addressed by many authors going all the way back to original developments by Richard Bellman. The basic idea of the involved dynamic principle is that a policy designed at the first stage, before observing realizations of the random data, should not be changed at the … Read more

    Exact and Inexact Subsampled Newton Methods for Optimization

  • Raghu Bollapragada
  • Richard H. Byrd
  • Jorge Nocedal
    • Categories Convex Optimization, Nonlinear Optimization, Stochastic Programming Tags ,

    The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of … Read more

    The Multilinear polytope for acyclic hypergraphs

  • Alberto Del Pia
  • Aida Khajavirad
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Global Optimization Theory Tags , , , ,

    We consider the Multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. Such sets are of fundamental importance in many types of mixed-integer nonlinear optimization problems, such as binary polynomial optimization. Utilizing an equivalent hypergraph representation, we study the facial structure of the Multilinear polytope … Read more