Applications – Science and Engineering

Gradient Projection Methods for Quadratic Programs and Applications in Training Support Vector Machines

  • Thomas Serafini
  • Luca Zanni
  • Gaetano Zanghirati
    • Categories Data-Mining, Quadratic Programming Tags , , , ,

    Gradient projection methods based on the Barzilai-Borwein spectral steplength choices are considered for quadratic programming problems with simple constraints. Well known nonmonotone spectral projected gradient methods and variable projection methods are discussed. For both approaches the behavior of different combinations of the two spectral steplengths is investigated. A nw adaptive stplength alternating rule is proposed, … Read more

    Reservoir Operation by Ant Colony Optimization Algorithms

  • Abbas Afshar
  • Mohammad Reza Jalali
  • M. A. Marino
    • Categories Civil and Environmental Engineering, Meta Heuristics

    In this paper, ant colony optimization (ACO) algorithms are proposed for reservoir operation. Through a collection of cooperative agents called ants, the nearoptimum solution to the reservoir operation can be effectively achieved. To apply ACO algorithms, the problem is approached by considering a finite horizon with a time series of inflow, classifying the reservoir volume … Read more

    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

    Error Estimates and Poisedness in Multivariate Polynomial Interpolation

  • Andrew R. Conn
  • Katya Scheinberg
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Nonlinear Optimization Tags , , ,

    We show how to derive error estimates between a function and its interpolating polynomial and between their corresponding derivatives. The derivation is based on a new definition of well-poisedness for the interpolation set, directly connecting the accuracy of the error estimates with the geometry of the points in the set. This definition is equivalent to … Read more

    The mathematics of eigenvalue optimization

  • Adrian Lewis
    • Categories Control Applications, Nonsmooth Optimization, Semi-definite Programming Tags , , , , , , , , , , , , , , , ,

    Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of some central mathematical ideas, outlined for … Read more

    Quasi-Newton methods for large-scale distributed parameter estimation

  • Eldad Haber
    • Categories Optimization of Systems modeled by PDEs Tags , ,

    We develop Quasi-Newton methods for distributed parameter estimation problems, where the forward problem is governed by a set of partial differential equations. A Tikhonov style regularization approach yields an optimization problem with a special structure, where the gradients are calculated using the adjoint method. In many cases standard Quasi-Newton methods (such as L-BFGS) are not … Read more

    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

    Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank

  • Leonid Faybusovich
  • Takashi Tsuchiya
    • Categories Control Applications, Linear, Cone and Semidefinite Programming Tags , , , ,

    We consider primal-dual algorithms for certain types of infinite-dimensional optimization problems. Our approach is based on the generalization of the technique of finite-dimensional Euclidean Jordan algebras to the case of infinite-dimensional JB-algebras of finite rank. This generalization enables us to develop polynomial-time primal-dual algorithms for “infinite-dimensional second-order cone programs.” We consider as an example a … Read more

    Effective reformulations of the truss topology design problem

  • Michal Kočvara
  • Jiri V. Outrata
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering, Nonlinear Optimization Tags ,

    We present a new formulation of the truss topology problem that results in unique design and unique displacements of the optimal truss. This is reached by adding an upper level to the original optimization problem and formulating the new problem as an MPCC (Mathematical Program with Complementarity Constraints). We derive optimality conditions for this problem … Read more