Global Optimization

Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
  • Jianfeng Liu
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization Tags , ,

    We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. … Read more

    Generalized Symmetric ADMM for Separable Convex Optimization

  • Jianchao Bai
  • Jicheng Li
  • Fengmin Xu
  • Hongchao Zhang
    • Categories Convex Optimization, Global Optimization Theory Tags , , , , , ,

    The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two … Read more

    Dynamic Spectrum Management: A Complete Complexity Characterization

  • Ya-Feng Liu
    • Categories Applications - OR and Management Sciences, Global Optimization Theory, Telecommunications Tags , , ,

    Consider a multi-user multi-carrier communication system where multiple users share multiple discrete subcarriers. To achieve high spectrum efficiency, the users in the system must choose their transmit power dynamically in response to fast channel fluctuations. Assuming perfect channel state information, two formulations for the spectrum management (power control) problem are considered in this paper: the … 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. ArticleDownload View PDF

    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

    Optimal Deterministic Algorithm Generation

  • Ioannis G. Kevrekidis
  • Alexander Mitsos
  • Jaromił Najman
    • Categories Applications - Science and Engineering, Global Optimization, Other Topics Tags , ,

    A formulation for the automated generation of algorithms via mathematical programming (optimization) is proposed. The formulation is based on the concept of optimizing within a parameterized family of algorithms, or equivalently a family of functions describing the algorithmic steps. The optimization variables are the parameters – within this family of algorithms- that encode algorithm design: … Read more

    Branch and Bound based methods to minimize the energy consumed by an electrical vehicle on long travels with slopes

  • Abdelkader Merakeb
  • Frédéric Messine
  • Riadh Omheni
    • Categories Applications - Science and Engineering, Global Optimization Tags , , , , ,

    We consider the problem of minimization of the energy consumed by an electrical vehicle performing quite long travels with slopes. The model we address here, takes into account the electrical and mechanical differential equations of the vehicle. This yields a mixed-integer optimal control problem that can be approximated, using a methodology based on some decomposition … Read more

    Global Optimization in Hilbert Space

  • Benoit Chachuat
  • Boris Houska
    • Categories Global Optimization Theory, Infinite Dimensional Optimization

    This paper proposes a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. … Read more

    A new branch-and-bound algorithm for standard quadratic programming problems

  • Giampaolo Liuzzi
  • Marco Locatelli
  • Veronica Piccialli
    • Categories Global Optimization, Quadratic Programming

    In this paper we propose convex and LP bounds for Standard Quadratic Programming (StQP) problems and employ them within a branch-and-bound approach. We first compare different bounding strategies for StQPs in terms both of the quality of the bound and of the computation times. It turns out that the polyhedral bounding strategy is the best … Read more

    Best subset selection for eliminating multicollinearity

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

    This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities … Read more