Resource Allocation for Contingency Planning: An Inexact Bundle Method for Stochastic Optimization

  • Ricardo A. Collado
  • Somayeh Moazeni
    • Categories Nonsmooth Optimization, Production and Logistics, Stochastic Programming Tags , , , ,

    Resource allocation models in contingency planning aim to mitigate unexpected failures in supply chains due to disruptions with rare occurrence but disastrous consequences. This paper formulates this problems as a two-stage stochastic optimization with a risk-averse recourse function, and proposes a novel computationally tractable solution approach. The method relies on an inexact bundle method and … Read more

    Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

  • Ahmadi-Javid Amir
  • Pooya Hoseinpour
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Second-Order Cone Programming

    Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be … Read more

    Minotaur: A Mixed-Integer Nonlinear Optimization Toolkit

  • Sven Leyffer
  • Jeff Linderoth
  • James R. Luedtke
  • Ashutosh Mahajan
  • Todd S. Munson
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Optimization Software and Modeling Systems Tags , ,

    We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more

    A Level-set Method For Convex Optimization with a Feasible Solution Path

  • Qihang Lin
  • Selvaprabu Nadarajah
  • Negar Soheili
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    Large-scale constrained convex optimization problems arise in several application domains. First-order methods are good candidates to tackle such problems due to their low iteration complexity and memory requirement. The level-set framework extends the applicability of first-order methods to tackle problems with complicated convex objectives and constraint sets. Current methods based on this framework either rely … Read more

    DSCOVR: Randomized Primal-Dual Block Coordinate Algorithms for Asynchronous Distributed Optimization

  • Weizhu Chen
  • Qihang Lin
  • Lin Xiao
  • Wei Yu
    • Categories Convex and Nonsmooth Optimization, Parallel Algorithms Tags , , , , ,

    Machine learning with big data often involves large optimization models. For distributed optimization over a cluster of machines, frequent communication and synchronization of all model parameters (optimization variables) can be very costly. A promising solution is to use parameter servers to store different subsets of the model parameters, and update them asynchronously at different machines … Read more

    Using Neural Networks to Detect Line Outages from PMU Data

  • Stephen Wright
  • Ching-pei Lee
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    We propose an approach based on neural networks and the AC power flow equations to identify single- and double- line outages in a power grid using the information from phasor measurement unit sensors (PMUs). Rather than inferring the outage from the sensor data by inverting the physical model, our approach uses the AC model to … Read more

    Novel Radar Waveform Optimization for a Cooperative Radar-Communications System

  • Daniel W. Bliss
  • Hans D Mittelmann
  • Alex R. Chiriyath
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering Tags , , , ,

    We develop and present the novel minimum estimation error variance waveform design method, that optimizes the spectral shape of a unimodular radar waveform such that the performance of a joint radar-communications system that shares spectrum is maximized. We also perform a numerical study to compare the performance of the new technique with the previously derived … Read more

    Enhanced Pseudo-Polynomial Formulations for Bin Packing and Cutting Stock Problems

  • Maxence Delorme
  • Manuel Iori
    • Categories (Mixed) Integer Linear Programming Tags , , , , ,

    We study pseudo-polynomial formulations for the classical bin packing and cutting stock problems. We first propose an overview of dominance and equivalence relations among the main pattern-based and pseudo-polynomial formulations from the literature. We then introduce reflect, a new formulation that uses just half of the bin capacity to model an instance and needs significantly … Read more

    Stochastic Dynamic Programming Using Optimal Quantizers

  • Georg Ch. Pflug
  • Anna Timonina-Farkas
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Stochastic Programming

    Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty, which applications include financial and investment planning, inventory control, energy production and trading, electricity generation planning, supply chain management and similar fields. Theoretical solution of multi-stage stochastic programs can be found explicitly only in very exceptional cases due to the complexity of the … Read more

    Using a Factored Dual in Augmented Lagrangian Methods for Semidefinite Programming

  • Marianna De Santis
  • Franz Rendl
  • Angelika Wiegele
    • Categories Linear, Cone and Semidefinite Programming Tags , ,

    In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further propose to use the approximate maximum of … Read more