(Mixed) Integer Nonlinear Programming

Socially optimal location of facilities with fixed servers, stochastic demand and congestion

  • Ignacio Castillo
  • Armann Ingolfsson
  • Thaddeus Sim
    • Categories (Mixed) Integer Nonlinear Programming, Multidisciplinary Design Optimization

    We present two capacity choice scenarios for the socially optimal location of facilities with fixed servers, stochastic demand and congestion. Walk-in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems are motivating examples of such facilities. The choice of locations for such facilities influences not only distances for users traveling … Read more

    Solving large MINLPs on computational grids

  • Jean-Pierre Goux
  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Parallel Algorithms Tags , , ,

    We consider the solution of Mixed Integer Nonlinear Programming (MINLP) problems by a parallel implementation of nonlinear branch-and-bound on a computational grid or meta-computer. Computational experience on a set of large MINLPs is reported which indicates that this approach is efficient for the solution of large MINLPs. Citation Numerical Analysis Report NA/200, Department of Mathematics, … Read more

    Pattern search algorithms for mixed variable programming

  • Charles Audet
  • John E. Dennis, Jr.
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization Tags , , , ,

    Many engineering optimization problems involve a special kind of discrete variable that {\em can} be represented by a number, but this representation has no significance. Such variables arise when a decision involves some situation like a choice from an unordered list of categories. This has two implications: The standard approach of solving problems with continuous … Read more

    Mixed variable optimization of the number and composition of heat intercepts in a thermal insulation system

  • Charles Audet
  • John E. Dennis, Jr.
  • Michael Kokkolaras
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization, Mechanical Engineering Tags , , , , ,

    In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization … Read more

    Generating Convex Polynomial Inequalities for Mixed 0-1 Programs

  • Sanjay Mehrotra
  • Robert Stubbs
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization, Global Optimization Theory Tags , , , ,

    We develop a method for generating valid convex polynomial inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities. Article Download View Generating Convex … Read more

    Integrating SQP and branch-and-bound for Mixed Integer Nonlinear Programming

  • Sven Leyffer
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming Tags , ,

    This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems. In … Read more