Mitigating Uncertainty via Compromise Decisions in Two-stage Stochastic Linear Programming

  • Suvrajeet Sen
  • Yifan Liu
    • Categories Stochastic Programming Tags , ,

    Stochastic Programming (SP) has long been considered as a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines … Read more

    A Block Successive Upper Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization

  • Tsung-Hui Chang
  • Zhi-Quan Luo
  • Shiqian Ma
  • Mingyi Hong
  • Meisam Razaviyayn
  • Xiangfeng Wang
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    Consider the problem of minimizing the sum of a smooth convex function and a separable nonsmooth convex function subject to linear coupling constraints. Problems of this form arise in many contemporary applications including signal processing, wireless networking and smart grid provisioning. Motivated by the huge size of these applications, we propose a new class of … Read more

    Distributed Optimization Methods for Large Scale Optimal Control

  • Attila Kozma
    • Categories Optimization of Simulated Systems, Quadratic Programming Tags , , , , ,

    This thesis aims to develop and implement both nonlinear and linear distributed optimization methods that are applicable, but not restricted to the optimal control of distributed systems. Such systems are typically large scale, thus the well-established centralized solution strategies may be computationally overly expensive or impossible and the application of alternative control algorithms becomes necessary. … Read more

    On QPCCs, QCQPs and Completely Positive Programs

  • Lijie Bai
  • John E. Mitchell
  • Jong-Shi Pang
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming

    This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a quadratically constrained quadratic program (QCQP), a quadratic program with complementarity constraints (QPCC), and rank constrained semidefinite programs. Our results … Read more

    Scheduling the Tasks of Two Agents with a Central Selection Mechanism

  • Gaia Nicosia
  • Ulrich Pferschy
  • Andrea Pacifici
    • Categories Combinatorial Optimization, Game Theory, Scheduling Tags , ,

    We address a class of deterministic scheduling problems in which two agents compete for the usage of a single machine. The agents have their own objective functions and submit in each round an arbitrary, unprocessed task from their buffer for possible selection. In each round the smaller of the two submitted tasks is chosen and … Read more

    Confidence Levels for CVaR Risk Measures and Minimax Limits

  • Edward Anderson
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming

    Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and its … Read more

    Alternating direction method of multipliers for sparse zero-variance discriminant analysis and principal component analysis

  • Brendan Ames
  • Mingyi Hong
    • Categories Data-Mining, Statistics

    We consider the task of classification in the high-dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose sparse zero-variance discriminant analysis (SZVD) as a method for simultaneouslyperforming linear discriminant analysis and feature selection on high-dimensional data. This method combines … Read more

    Constraint Programming for LNG Ship Scheduling and Inventory Management

  • Kevin C Furman
  • Willem-Jan van Hoeve
  • Vikas Goel
  • Yufen Shao
  • Marla Slusky
    • Categories Production and Logistics, Supply Chain Management, Transportation Tags , ,

    We propose a constraint programming approach for the optimization of inventory routing in the liquefied natural gas industry. We present two constraint programming models that rely on a disjunctive scheduling representation of the problem. We also propose an iterative search heuristic to generate good feasible solutions for these models. Computational results on a set of … Read more

    Eigenvalue, Quadratic Programming, and Semidefinite Programming Relaxations for a Cut Minimization Problem

  • Ting Kei Pong
  • Henry Wolkowicz
  • Hao Sun
  • Ningchuan Wang
    • Categories Combinatorial Optimization, Graphs and Matroids, Semi-definite Programming Tags , , , ,

    We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex separator. This problem is closely related to the graph partitioning problem. In … Read more

    Extreme point inequalities and geometry of the rank sparsity ball

  • Dmitriy Drusvyatskiy
  • Stephen A. Vavasis
  • Henry Wolkowicz
    • Categories Convex Optimization Tags , , , , ,

    We investigate geometric features of the unit ball corresponding to the sum of the nuclear norm of a matrix and the l_1 norm of its entries — a common penalty function encouraging joint low rank and high sparsity. As a byproduct of this effort, we develop a calculus (or algebra) of faces for general convex … Read more