Global Optimization Applications

An Algorithm for Stochastic Convex-Concave Fractional Programs with Applications to Production Efficiency and Equitable Resource Allocation

  • Cheolmin Kim
  • Sanjay Mehrotra
    • Categories Global Optimization, Global Optimization Applications, Stochastic Approaches Tags , , , ,

    We propose an algorithm to solve convex and concave fractional programs and their stochastic counterparts in a common framework. Our approach is based on a novel reformulation that involves differences of square terms in the constraints, and subsequent employment of piecewise-linear approximations of the concave terms. Using the branch-and-bound framework, our algorithm adaptively refines the … Read more

    MatQapNB User Guide: A branch-and-bound program for QAPs in Matlab with the Newton-Bracketing method

  • Koichi Fujii
  • Naoki Ito
  • Sunyoung Kim
  • Masakazu Kojima
  • Hans D Mittelmann
  • Kim-Chuan Toh
  • Yuji Shinano
    • Categories Global Optimization Applications, Optimization Software Design Principles, Quadratic Programming Tags , , ,

    MatQapNB is a MATLAB toolbox that implements a parallel branch-and-bound method using NewtBracket (the Newton bracketing method [4]) for its lower bounding procedure. It can solve small to medium scale Quadratic Assignment Problem (QAP) instances with dimension up to 30. MatQapNB was used in the numerical experiments on QAPs in the recent article “Solving challenging … Read more

    Penetration depth between two convex polyhedra: An efficient global optimization approach

  • Mark A. Abramson
  • Griffin D. Kent
  • Gavin W. Smith
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Applications Tags , , , ,

    During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, … Read more

    Recent Advances in Nonconvex Semi-infinite Programming: Applications and Algorithms

  • Hatim Djelassi
  • Alexander Mitsos
  • Oliver Stein
    • Categories Global Optimization Applications, Semi-infinite Programming

    The goal of this literature review is to give an update on the recent developments for semi-infinite programs (SIPs), approximately over the last 20 years. An overview of the different solution approaches and the existing algorithms is given. We focus on deterministic algorithms for SIPs which do not make any convexity assumptions. In particular, we … Read more

    Mathematical Programming formulations for the Alternating Current Optimal Power Flow problem

  • Daniel Bienstock
  • Mauro Escobar
  • Claudio Gentile
  • Leo Liberti
    • Categories Energy, Global Optimization Applications, Quadratic Programming Tags , ,

    Power flow refers to the injection of power on the lines of an electrical grid, so that all the injections at the nodes form a consistent flow within the network. Optimality, in this setting, is usually intended as the minimization of the cost of generating power. Current can either be direct or alternating: while the … Read more

    Cycle-based formulations in Distance Geometry

  • Gabriele Iommazzo
  • Carlile Lavor
  • Leo Liberti
  • Nelson Maculan
    • Categories Biomedical Applications, Global Optimization Applications, Quadratic Programming Tags , ,

    The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the edge weights. The problem is often modelled as a mathematical programming formulation involving decision … Read more

    Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems

  • Giampaolo Liuzzi
  • Marco Locatelli
  • Veronica Piccialli
  • Stefan Rass
    • Categories Game Theory, Global Optimization Applications, Quadratic Programming

    In this paper we address a game theory problem arising in the context of network security. In traditional game theory problems, given a defender and an attacker, one searches for mixed strategies which minimize a linear payoff functional. In the problem addressed in this paper an additional quadratic term is added to the minimization problem. … Read more

    Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

  • Gratien Bonvin
  • Andrea Lodi
  • Sophie Demassey
    • Categories Global Optimization Applications Tags , , ,

    This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints … Read more

    A new discrete filled function with generic local searches for global nonlinear integer optimization

  • J Di Mauro
  • HD Scolnik
    • Categories Global Optimization Applications, Global Optimization Theory Tags , , ,

    The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However, they rely on the steepest descent method for local searches. Here we present an approach that does not … Read more

    On tackling reverse convex constraints for non-overlapping of unequal circles

  • Chrysanthos E. Gounaris
  • Akang Wang
    • Categories Global Optimization, Global Optimization Applications Tags , , , , ,

    We study the unequal circle-circle non-overlapping constraints, a form of reverse convex constraints that often arise in optimization models for cutting and packing applications. The feasible region induced by the intersection of circle-circle non-overlapping constraints is highly non-convex, and standard approaches to construct convex relaxations for spatial branch-and-bound global optimization of such models typically yield … Read more