Nonlinear Optimization

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

    Additional properties of shifted valiable metric methods.

  • Ladislav Lukšan
  • Jan Vlček
    • Categories Unconstrained Optimization Tags , , , ,

    Some supplements to shifted variable metric or quasi-Newton methods for unconstrained minimization are given, including new limited-memory methods. Global convergence of these methods can be established for convex sufficiently smooth functions. Some encouraging numerical experience is reported. CitationReport No. V899-03, Institute of Computer Scienc, Czech Academy of Sciences, Prague, December 2003 (revised May 2004).ArticleDownload View … Read more

    Necessary and Sufficient Optimality Conditions for Mathematical Programs with Equilibrium Constraints

  • Jane J. Ye
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this paper we consider a mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with complementarity constraints. Various stationary conditions for MPECs exist in literature due to different reformulations. We give a simple proof to the M-stationary condition and show that it is sufficient or locally sufficient for optimality under some MPEC … Read more

    On the Relationship Between Convergence Rates of Discrete and Continuous Dynamical Systems

  • Raphael Hauser
  • Jelena Nedic
    • Categories Unconstrained Optimization Tags ,

    Considering iterative sequences that arise when the approximate solution $x_k$ to a numerical problem is updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a vector field, we derive necessary and sufficient conditions for such discrete methods to converge to a stationary point of $v$ at different Q-rates in terms of the differential properties of $v$ … Read more

    A modified nearly exact method for solving low-rank trust region subproblem

  • Zhaosong Lu
  • Renato D.C. Monteiro
    • Categories Nonlinear Optimization Tags , , , ,

    In this paper we present a modified nearly exact (MNE) method for solving low-rank trust region (LRTR) subproblem. The LRTR subproblem is to minimize a quadratic function, whose Hessian is a positive diagonal matrix plus explicit low-rank update, subject to a Dikin-type ellipsoidal constraint, whose scaling matrix is positive definite and has the similar structure … Read more

    Optimality Measures for Performance Profiles

  • Elizabeth D. Dolan
  • Jorge Moré
  • Todd S. Munson
    • Categories Nonlinear Optimization Tags ,

    We examine the importance of optimality measures when benchmarking a set of solvers, and show that scaling requirements lead to a convergence test for nonlinearly constrained optimization solvers that uses a mixture of absolute and relative error measures. We demonstrate that this convergence test is well behaved at any point where the constraints satisfy the … Read more

    Benchmarking Optimization Software with COPS 3.0

  • Elizabeth D. Dolan
  • Jorge Moré
  • Todd S. Munson
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark

    We describe version 3.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the FILTER, KNITRO, LOQO, MINOS, and SNOPT solvers on these problems. CitationTechnical Report ANL/MCS-TM-273, Argonne National Laboratory, 02/04.ArticleDownload View PDF

    A sequential quadratic programming algorithm with a piecewise linear merit function

  • Francisco Gomes
    • Categories Constrained Nonlinear Optimization Tags , ,

    A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays … Read more

    An Iterative Solver-Based Infeasible Primal-Dual Path-Following Algorithm for Convex QP

  • Zhaosong Lu
  • Renato D.C. Monteiro
  • Jerome W. O'Neal
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , ,

    In this paper we develop an interior-point primal-dual long-step path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of an iterative (linear system) solver. We propose a new linear system, which we refer to as the \emph{augmented normal equation} (ANE), to determine the primal-dual search directions. Since the condition number … Read more

    A Local Convergence Analysis of Bilevel Decomposition Algorithms

  • Victor DeMiguel
  • Walter Murray
    • Categories Multidisciplinary Design Optimization, Nonlinear Optimization Tags , , ,

    Decomposition algorithms exploit the structure of large-scale optimization problems by breaking them into a set of smaller subproblems and a coordinating master problem. Cutting-plane methods have been extensively used to decompose convex problems. In this paper, however, we focus on certain nonconvex problems arising in engineering. Engineers have been using bilevel decomposition algorithms to tackle … Read more