Now showing items 1-10 of 67
On the Quadratic Convergence of the Singular Newton's Method
The purpose of this essay is to describe a situation that we have found particularly exciting in our recent work in interior-point methods for linear programming. To our surprise, we have seen considerable theory developed ...
An Interior-Point Method with Polynomial Complexity and Superlinear Convergence for Linear Complementarity Problems
For linear programming, a primal-dual interior-point algorithm was recently constructed by Zhang and Tapia that achieves both polynomial complexity and Q-superlinear convergence (Q-quadratic in the nondegenerate case). In ...
User's Guide for LMaFit: Low-rank Matrix Fitting
This User's Guide describes the functionality and basic usage of the Matlab package LMaFit for low-rank matrix optimization. It also briefly explains the formulations and algorithms used.
Solving Semidefinite Programs via Nonlinear Programming, Part I: Transformations and Derivatives
In this paper, we introduce transformations that convert a large class of linear and/or nonlinear semidefinite programming (SDP) problems into nonlinear optimization problems over "orthants" of the form (R^n)++ × R^N, ...
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 ...
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 ...
Simultaneous Structure Factor and Contrast Transfer Function Parameter Determination in Transmission Electron Microscopy
We present a new method that allows a fully automated simultaneous determination of the structure factor and the parameters of the Contrast Transfer Function (CTF) and noise function. No previous knowledge of the structure ...
A Computational Study of a Gradient-Based Log-Barrier Algorithm for a Class of Large-Scale SDPs
The authors of this paper recently introduced a transformation that converts a class of semidefinite programs (SDPs) into nonlinear optimization problems free of matrix-valued constraints and variables. This transformation ...
Solving the Double Digestion Problem as a Mixed-Integer Linear Program
The double digestion problem for DNA restriction mapping is known to be NP-complete. Several approaches to the problem have been used including exhaustive search, simulated annealing, branch-and-bound. In this paper, we ...