Applications – Science and Engineering

The Design and Implementation of a Generic Sparse Bundle Adjustment Software Package Based on the Levenberg-Marquardt Algorithm

  • Antonis Argyros
  • Manolis Lourakis
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Optimization Software and Modeling Systems Tags , , , , ,

    Bundle adjustment using the Levenberg-Marquardt minimization algorithm is almost invariably used as the last step of every feature-based structure and motion estimation computer vision algorithm to obtain optimal 3D structure and viewing parameter estimates. However, due to the large number of unknowns contributing to the minimized reprojection error, a general purpose implementation of the Levenberg-Marquardt … Read more

    Optimal distance separating halfspace

  • Emilio Carrizosa
  • Frank Plastria
    • Categories Data-Mining, Global Optimization Applications Tags , ,

    One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm,while misclassification means lying on the wrong side of the hyperplane, or … Read more

    Optimal expected-distance separating halfspace

  • Emilio Carrizosa
  • Frank Plastria
    • Categories Data-Mining, Global Optimization Applications, Statistics Tags , ,

    One recently proposed criterion to separate two datasets in discriminant analysis, is to use a hyperplane which minimises the sum of distances to it from all the misclassified data points. Here all distances are supposed to be measured by way of some fixed norm, while misclassification means lying on the wrong side of the hyperplane, … Read more

    A survey of the S-lemma

  • Imre Pólik
  • Tamás Terlaky
    • Categories Control Applications, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , , , ,

    In this survey we review the many faces of the S-lemma, a result about the correctness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as … Read more

    Performance of CONDOR, a Parallel, Constrained extension of Powell’s UOBYQA algorithm. Experimental results and comparison with the DFO algorithm.

  • Hugues Bersini
  • Frank Vanden Berghen
    • Categories Constrained Nonlinear Optimization, Optimization of Systems modeled by PDEs, Parallel Algorithms Tags , , ,

    This paper presents an algorithmic extension of Powell’s UOBYQA algorithm (”Unconstrained Optimization BY Quadratical Approximation”). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the … Read more

    Recursive Trust-Region Methods for Multilevel Nonlinear Optimization (Part I): Global Convergence and Complexity

  • Serge Gratton
  • Annick Sartenaer
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization, Unconstrained Optimization Tags , , , ,

    A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a mean of speeding up the computation of the step. This use is recursive, leading to … Read more

    Second-order Cone Programming Methods for Total Variation-based Image Restoration

  • Donald Goldfarb
  • Wotao Yin
    • Categories Basic Sciences Applications, Second-Order Cone Programming Tags , , , , ,

    In this paper we present optimization algorithms for image restoration based on the total variation (TV) minimization framework of L. Rudin, S. Osher and E. Fatemi (ROF). Our approach formulates TV minimization as a second-order cone program which is then solved by interior-point algorithms that are efficient both in practice (using nested dissection and domain … Read more

    GLOBAL CONVERGENCE OF AN ELASTIC MODE APPROACH FOR A CLASS OF MATHEMATICAL PROGRAMS WITH COMPLEMENTARITY CONSTRAINTS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Mechanical Engineering Tags , , ,

    We prove that any accumulation point of an elastic mode approach, applied to the optimization of a mixed P variational inequality, that approximately solves the relaxed subproblems is a C-stationary point of the problem of optimizing a parametric mixed P variational inequality. If, in addition, the accumulation point satis es the MPCC-LICQ constraint quali cation and if … Read more

    OPTIMIZATION-BASED SIMULATION OF NONSMOOTH RIGID MULTIBODY DYNAMICS

  • Mihai Anitescu
    • Categories Complementarity and Variational Inequalities, Mechanical Engineering Tags , , , ,

    We present a time-stepping method to simulate rigid multibody dynamics with inelastic collision, contact, and friction. The method progresses with fixed time step without backtracking for collision and solves at every step a strictly convex quadratic program. We prove that a solution sequence of the method converges to the solution of a measure differential inclusion. … Read more

    Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

  • Frederic Delbos
  • Jean Charles Gilbert
  • R. Glowinski
  • D. Sinoquet
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming Tags , , , , , ,

    Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more