Now showing items 251-260 of 265
A Fast Newton's Algorithm for Entropy Maximization in Phase Determination
A long-standing problem in X-ray crystallography, known as the phase problem, is to determine the phases for a large set of complex variables, called the structure factors of the crystal, given their magnitudes obtained ...
The Sphere of Convergence of Newton's Method on Two Equivalent Systems from Nonlinear Programming
We study a local feature of a Newton logarithmic barrier function method and a Newton primal-dual interior-point method. In particular, we study the radius of the sphere of convergence of Newton's method on two equivalent ...
Properties of A Class of Preconditioners for Weighted Least Squares Problems
A sequence of weighted linear least squares problems arises from interior-point methods for linear programming where the changes from one problem to the next are the weights and the right hand side. One approach for solving ...
On Convergence of Minimization Methods: Attraction, Repulsion and Selection
In this paper, we introduce a rather straightforward but fundamental observation concerning the convergence of the general iteration process. x^(k+1) = x^k - alpha(x^k) [B(x^k)]^(-1) gradf(x^k) for minimizing a function ...
Convergence Results for Pattern Search Algorithms are Tight
Recently, general definitions of pattern search methods for both unconstrained and linearly constrained optimization were presented. It was shown under mild conditions, that there exists a subsequence of iterates converging ...
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
We present a matrix-free algorithm for the large-scale trust-region subproblem. Our algorithm relies on matrix-vector products only and does not require matrix factorizations. We recast the trust-region subproblem as a ...
Implementing Nonlinear Operators in HCL
An Overview of HCL 1.0
The Hilbert Class Library (HCL) is a collection of C++ classes which apply object-oriented programming principles to implement mathematical objects such as vectors, linear and nonlinear operators, and functions. HCL provides ...
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 ...
Solving Semidefinite Programs via Nonlinear Programming, Part II: Interior Point Methods for a Subclass of SDPs
In Part I of this series of papers, we have introduced transformations which convert a large class of linear and nonlinear semidefinite programs (SDPs) into nonlinear optimization problems over "orthants" of the form ...