Month: September 2016

An Infeasible Active Set Method with Combinatorial Line Search for Convex Quadratic Problems with Bound Constraints

  • Philipp Hungerländer
  • Franz Rendl
    • Categories Convex Optimization, Quadratic Programming Tags , , , ,

    The minimization of a convex quadratic function under bound constraints is a fundamental building block for more complicated optimization problems. The active-set method introduced by [M. Bergounioux, K. Ito, and K. Kunisch. Primal-Dual Strategy for Constrained Optimal Control Problems. SIAM Journal on Control and Optimization, 37:1176–1194, 1999.] and [M. Bergounioux, M. Haddou, M. Hintermüller, and … Read more

    An Effective Dynamic Programming Algorithm for the Minimum-Cost Maximal Knapsack Packing

  • Fabio Furini
  • Ivana Ljubić
  • Markus Sinnl
    • Categories Combinatorial Optimization, Dynamic Programming, Integer Programming

    Given a set of n items with profits and weights and a knapsack capacity C, we study the problem of finding a maximal knapsack packing that minimizes the profit of selected items. We propose for the first time an effective dynamic programming (DP) algorithm which has O(nC) time complexity and O(n+C) space complexity. We demonstrate … Read more

    On deterministic reformulations of distributionally robust joint chance constrained optimization problems

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more

    A universal and structured way to derive dual optimization problem formulations

  • Marleen Balvert
  • Dick den Hertog
  • Bram L. Gorissen
  • Cornelis Roos
    • Categories Convex Optimization Tags , , , ,

    The dual problem of a convex optimization problem can be obtained in a relatively simple and structural way by using a well-known result in convex analysis, namely Fenchel’s duality theorem. This alternative way of forming a strong dual problem is the subject in this paper. We recall some standard results from convex analysis and then … Read more

    Optimization with stochastic preferences based on a general class of scalarization functions

  • Nilay Noyan
  • Gabor Rudolf
    • Categories Multi-Criteria Optimization, Stochastic Programming

    It is of crucial importance to develop risk-averse models for multicriteria decision making under uncertainty. A major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints. These problems typically involve a univariate stochastic preference relation, often based on stochastic dominance or a coherent risk measure such as conditional value-at-risk (CVaR), … Read more

    Decomposition and Optimization in Constructing Forward Capacity Market Demand Curves

  • Eugene Litvinov
  • Feng Zhao
  • Tongxin Zheng
    • Categories Applications - Science and Engineering, Finance and Economics Tags , , , , , , ,

    This paper presents an economic framework for designing demand curves in Forward Capacity Market (FCM). Capacity demand curves have been recognized as a way to reduce the price volatility inherited from fixed capacity requirements. However, due to the lack of direct demand bidding in FCM, obtaining demand curves that appropriately reflect load’s willingness to pay … Read more

    On the convergence of a regularized Jacobi algorithm for convex optimization

  • Goran Banjac
  • Paul J. Goulart
  • Kostas Margellos
    • Categories Nonsmooth Optimization Tags , , ,

    In this paper we consider the regularized version of the Jacobi algorithm, a block coordinate descent method for convex optimization with differentiable objective function and block-separable constraints that has been recently proposed in the literature. Under certain regularity assumptions on the objective function, this algorithm has been shown to satisfy the so-called sufficient decrease condition, … Read more

    Accelerated gradient sliding for structured convex optimization

  • Guanghui Lan
  • Yuyuan Ouyang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show … Read more

    Positive-Indefinite Proximal Augmented Lagrangian Method and its Application to Full Jacobian Splitting for Multi-block Separable Convex Minimization Problems

  • Bingsheng He
  • Feng Ma
  • Xiao-Ming Yuan
    • Categories Convex Optimization Tags , , , , , ,

    The augmented Lagrangian method (ALM) is fundamental for solving convex programming problems with linear constraints. The proximal version of ALM, which regularizes ALM’s subproblem over the primal variable at each iteration by an additional positive-definite quadratic proximal term, has been well studied in the literature. In this paper, we show that it is not necessary … Read more

    Ambiguous Risk Constraints with Moment and Unimodality Information

  • Ruiwei Jiang
  • Bowen Li
  • Johanna L. Mathieu
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    Optimization problems face random constraint violations when uncertainty arises in constraint parameters. Effective ways of controlling such violations include risk constraints, e.g., chance constraints and conditional Value-at-Risk (CVaR) constraints. This paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous. In particular, we assume that the distributional … Read more