Now showing items 11-20 of 719
A View of Unconstrained Optimization
Finding the unconstrained minimizer of a function of more than one variable is an important problem with many practical applications, including data fitting, engineering design, and process control. In addition, techniques ...
On Numerical Solution of the Maximum Volume Ellipsoid Problem
In this paper we study practical solution methods for finding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in R n defined by a finite set of affine inequalities. Our goal is to design a ...
Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computation
The convergence of Krylov subspace eigenvalue algorithms can be robustly measured by the angle the approximating Krylov space makes with a desired invariant subspace. This paper describes a new bound on this angle that ...
Interior-Point Algorithms for Semidefinite Programming Based on A Nonlinear Programming Formulation
Recently, the authors of this paper introduced a nonlinear transformation to convert the positive definiteness constraint on an n × n matrix function of a certain form into the positivity constraint on n scalar variables ...
Least-Change Secant Update Methods with Inaccurate Secant Conditions
In this paper, we investigate the role of the secant or quasi-Newton condition in the sparse Broyden or Schubert update method for solving systems of nonlinear equations whose Jacobians are either sparse, or can be approximated acceptably by conveniently sparse matrices. We develop a general theory on perturbations to the secant equation that will still allow a proof of local q-linear convergence. To illustrate the theory, we show how to generalize the standard secant condition to the case when the function difference is contaminated by noise....
All Stationary Points of Differential Semblance Are Asymptotic Global Minimizers: Layered Acoustics
Differential semblance velocity estimators have well-defined and smooth high frequency asymptotics. A version appropriate for analysis of CMP gathers and layered acoustic models has no secondary minima. Its structure ...
Local Analysis of Inexact Quasi-Newton Methods
Quasi-Newton methods are well known iterative methods for solving nonlinear problems. At each stage, a system of linear equations has to be solved. However, for large scale problems, solving the linear system of equations ...
RUF 1.0 User Manual
A Trust Region Strategy for Nonlinear Equality Constrained Optimization
Many current algorithms for nonlinear constrained optimization problems determine a direction by solving a quadratic programming subproblem. The global convergence properties are addressed by using a line search technique ...
A Large-Scale Trust-Region Approach to the Regularization of Discrete Ill-Posed Problems
We consider the problem of computing the solution of large-scale discrete ill-posed problems when there is noise in the data. These problems arise in important areas such as seismic inversion, medical imaging and signal ...