Global Optimization

Mathematical optimization for the inverse problem of intensity modulated radiation therapy

  • Yair Censor
    • Categories Biomedical Applications, Global Optimization Applications Tags , , , , ,

    In this tutorial we discuss modeling issues in intensity modulated radiation therapy, contrasting the continuous model with the fully-discretized one and considering feasibility formulations versus optimization setups. We review briefly some mathematical optimization techniques for IMRT. These include global optimization, multi-objective optimization, linear and mixed integer programming and projection methods. Citation in: J.R. Palta and … Read more

    The global optimization of Morse clusters by potential energy transformations

  • Jon P. K. Doye
  • Marco Locatelli
  • Robert H. Leary
  • Fabio Schoen
    • Categories Basic Sciences Applications, Biomedical Applications, Stochastic Approaches

    The Morse potential is a simple model pair potential that has a single parameter $\rho$ which determines the width of the potential well and allows a wide variety of materials to be modelled. Morse clusters provide a particularly tough test system for global optimization algorithms, and one that is highly relevant to methods that are … Read more

    D.C. Versus Copositive Bounds for Standard QP

  • Kurt M. Anstreicher
  • Samuel Burer
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , ,

    The standard quadratic program (QPS) is $\min_{x\in\Delta} x’Qx$, where $\Delta\subset\Re^n$ is the simplex $\Delta=\{ x\ge 0 : \sum_{i=1}^n x_i=1 \}$. QPS can be used to formulate combinatorial problems such as the maximum stable set problem, and also arises in global optimization algorithms for general quadratic programming when the search space is partitioned using simplices. One … Read more

    Global optimization of rational functions: a semidefinite programming approach

  • Etienne de Klerk
  • Dorina Jibetean
    • Categories Global Optimization Theory, Nonlinear Optimization, Semi-definite Programming Tags , , ,

    We consider the problem of global minimization of rational functions on $\LR^n$ (unconstrained case), and on an open, connected, semi-algebraic subset of $\LR^n$, or the (partial) closure of such a set (constrained case). We show that in the univariate case ($n=1$), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced … Read more

    SIAG/Opt Views-and-News Vol 14 No 1

  • Jos F. Sturm
  • Nicholas I. M. Gould
  • Ekkehard Sachs
  • Lorenz T. Biegler
  • Andreas Wächter
  • Sven Leyffer
  • Michael Bussieck
  • Armin Pruessner
    • Categories Complementarity and Variational Inequalities, Global Optimization, Nonlinear Optimization Tags ,

    SIAM’s SIAG/Opt Newsletter special issue on Large Scale Nonconvex Optimization. Guest editors Sven Leyffer and Jorge Nocedal, with contributions by Gould, Sachs, Biegler, Waechter, Leyffer, Bussieck and Pruessner. Citation SIAG/Opt Views-and-News, Volume 14 Number 1, April 2003. http://fewcal.uvt.nl/sturm/siagopt/ Article Download View SIAG/Opt Views-and-News Vol 14 No 1

    A Multicriteria Approach to Bilevel Optimization

  • Jörg Fliege
  • Luis Nunes Vicente
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    In this paper we study the relationship between bilevel optimization and bicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem … Read more

    Global Optimization of Homogeneous Polynomials on the Simplex and on the Sphere

  • Leonid Faybusovich
    • Categories Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags , ,

    We obtain rigorous estimates for linear and semidefinite relaxations of global optimization problems on the simplex and on the sphere Citation Research report, February, 2003 Article Download View Global Optimization of Homogeneous Polynomials on the Simplex and on the Sphere

    A randomized global optimization method for protein-protein docking

  • Bernardetta Addis
  • Fabio Schoen
    • Categories Biomedical Applications, Global Optimization Applications, Stochastic Approaches Tags , ,

    In this paper we report results on the problem of docking two large proteins by means of a two-phase monotonic basin hopping method. Given an appropriate force field which is used to measure the interaction energy between two biomolecules which are considered as rigid bodies, we used a randomized global optimization methods based upon the … Read more

    New global optima for Morse clusters at $\rho=8$

  • Marco Locatelli
  • Fabio Schoen
    • Categories Basic Sciences Applications, Stochastic Approaches Tags , ,

    We recently discovered 5 new putative globally optimum configurations for Morse clusters at $\rho=8$. This report contains some algorithmic details as well as the structures determined with our method. Citation Technical Report DSI 3-2003, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Firenze, 2003. Article Download View New global optima for Morse clusters … Read more

    A fast swap-based local search procedure for location problems

  • Mauricio G.C. Resende
  • Renato F. Werneck
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Global Optimization Applications Tags , ,

    We present a new implementation of a widely used swap-based local search procedure for the P-median problem, proposed in 1968 by Teitz and Bart. Our method produces the same output as the best alternatives described in the literature and, even though its worst-case complexity is similar, it can be significantly faster in practice: speedups of … Read more