Year: 2018

Exploiting Low-Rank Structure in Semidefinite Programming by Approximate Operator Splitting

  • Joaquim Dias Garcia
  • Mario Souto
  • Alvaro Viega
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Semi-definite Programming Tags , , , , ,

    In contrast with many other convex optimization classes, state-of-the-art semidefinite programming solvers are yet unable to efficiently solve large scale instances. This work aims to reduce this scalability gap by proposing a novel proximal algorithm for solving general semidefinite programming problems. The proposed methodology, based on the primal-dual hybrid gradient method, allows the presence of … Read more

    POLO: a POLicy-based Optimization library

  • Arda Aytekin
  • Martin Biel
  • Mikael Johansson
    • Categories Convex and Nonsmooth Optimization, Optimization Software Design Principles, Parallel Algorithms Tags , , , ,

    We present POLO — a C++ library for large-scale parallel optimization research that emphasizes ease-of-use, flexibility and efficiency in algorithm design. It uses multiple inheritance and template programming to decompose algorithms into essential policies and facilitate code reuse. With its clear separation between algorithm and execution policies, it provides researchers with a simple and powerful … Read more

    Delay and disruption management at ATM: technical details

  • Federico Malucelli
  • Emanuele Tresoldi
    • Categories Applications - OR and Management Sciences, Transportation Tags , , , , ,

    Most of the local public transit companies have vehicle monitoring systems able to collect huge quantities of data in real-time. Typically, these data are used to measure the performance of the transportation system, and rarely they are fully exploited to improve it and to tackle disruptions. In this report we take into consideration the case … Read more

    Assessing the Cost of the Hazard-Decision Simplification in Multistage Stochastic Hydrothermal Scheduling

  • Andre Lawson
  • Alexandre Street
  • Davi Valladão
  • Alexandre Velloso
    • Categories Control Applications, Dynamic Programming, Stochastic Programming Tags , , ,

    Hydropower is one of the world’s primary renewable energy sources whose usage has profound economic, environmental, and social impacts. We focus on the dispatch of generating units and the storage policy of hydro resources. In this context, an accurate assessment of the water opportunity-cost is cru- cial for driving the sustainable use of this scarce … Read more

    Non-convex min-max fractional quadratic problems under quadratic constraints: copositive relaxations

  • Paula Alexandra Amaral
  • Immanuel M. Bomze
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , , ,

    In this paper we address a min-max problem of fractional quadratic (not necessarily convex) over linear functions on a feasible set described by linear and (not necessarily convex) quadratic functions. We propose a conic reformulation on the cone of completely positive matrices. By relaxation, a doubly non negative conic formulation is used to provide lower … Read more

    Decision Diagrams for Solving Traveling Salesman Problems with Pickup and Delivery in Real Time

  • Karla Hoffman
  • Ryan J. O'Neil
    • Categories Transportation

    The Traveling Salesman Problem with Pickup and Delivery seeks a minimum cost path with pickups preceding deliveries. It is important in on-demand last-mile logistics, such as ride sharing and meal delivery. We examine the use of low-width Decision Diagrams in a branch-and-bound with and without Assignment Problem inference duals as a primal heuristic for finding … Read more

    Multi-Stage Stochastic Programming Models for Provisioning Cloud Computing Resources

  • Kerem Bülbül
  • Nilay Noyan
  • Hazal Erol
    • Categories Applications - OR and Management Sciences, Stochastic Programming

    We focus on the resource provisioning problem of a cloud consumer from an Infrastructure-as-a-Service type of cloud. The cloud provider offers two deployment options, which can be mixed and matched as appropriate. Cloud instances may be reserved for a fixed time period in advance at a smaller usage cost per hour but require a full … Read more

    Dynamic Optimization with Convergence Guarantees

  • Eric C. Kerrigan
  • Martin Neuenhofen
    • Categories Infinite Dimensional Optimization, Systems governed by Differential Equations Optimization

    We present a novel direct transcription method to solve optimization problems subject to nonlinear differential and inequality constraints. In order to provide numerical convergence guarantees, it is sufficient for the functions that define the problem to satisfy boundedness and Lipschitz conditions. Our assumptions are the most general to date; we do not require uniqueness, differentiability … Read more

    Empirical Bounds on Linear Regions of Deep Rectifier Networks

  • Srikumar Ramalingam
  • Thiago Serra
    • Categories (Mixed) Integer Linear Programming, Statistics

    One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for … Read more

    Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems under Demand Uncertainty

  • Chrysanthos E. Gounaris
  • Anirudh Subramanyam
  • Panagiotis P. Repoussis
    • Categories Robust Optimization, Transportation Tags , , , , ,

    This paper studies robust variants of an extended model of the classical Heterogeneous Vehicle Routing Problem (HVRP), where a mixed fleet of vehicles with different capacities, availabilities, fixed costs and routing costs is used to serve customers with uncertain demand. This model includes, as special cases, all variants of the HVRP studied in the literature … Read more