Henry Wolkowicz's Research

Research Home
Publications & Abstracts
Talks & Presentations
and SNL



Misc. Software/Opt. Matrices

Nonlinear Programming


Regularization and Trust Region Subproblem

Three Master's Theses: A directory with the MATLAB software for the regularization from the above thesis of Oleg Grodzevich. (See the demo file -- but you will need the Hansen package for this demo file.) The dll files are available for Windows MATLAB.
A directory with the MATLAB software for the trust region subproblem related to the above thesis of Charles Fortin.
A list of home pages in Regularization and related areas:
Informatics and mathematical modelling at Technical University of Denmark
Contains MOORE TOOLS, an object oriented toolbox for Matlab,
and Regularization Tools, a MATLAB package by Prof Per Christian Hansen.



Nonlinear Programming

Two popular methods for unconstrained minimization are: Trust Region methods and Quasi-Newton methods. 

Trust Region Subproblems consist in minimizing a quadratic function subject to a quadratic constraint. This directory contains programs for solving the trust region subproblem. This routine is in MATLAB. It uses the MATLAB eigs function, i.e., it finds the smallest eigenvalue using the Lanczos algorithm. This program can solve large sparse problems very quickly. The research report is available.

Also available are two related research reports:
Indefinite trust region subproblems provide characterizations of optimality and relations to perturbed eigenvalue problems for the case where both the objective and constraint can be indefinite;

Nonsymmetric eigenvalue perturbations provides relationships between trust region subproblems and eigenvalue perturbations.
Quasi-Newton Methods or Least Change Secant Methods are based on approximating the Hessian using gradient information. The following three papers deal with measures for finding best Hessian approximations:
Sizing and Least Change Secant Methods
Measures for Symmetric Rank-One Updates
An All Inclusive Efficient Region of Updates for Least Change Secant Methods

Also available
Measures for Least Change Secant Methods,
Master's thesis of Qing Zhao.

Bibliography for Optimization with Sensitivity Analysis,
long list of links related to sensitivity analysis.



Nonlinear Programming

Semidefinite Programming Applied to Nonlinear Programming is a Master's Thesis by Serge Kruk, a preliminary to an SQQP algorithm; also available is a Research Report on an SQQP algorithm.

A list of home pages in nonlinear programming and related areas;
COPS, Large-Scale Nonlinearly Constrained Optimization Problems; for developing test problems.

HQP is a solver for nonlinearly constrained large-scale optimization.

FSQP is a code for Feasible Sequential Quadratic Programming.

A reading course on nonlinear programming was held during  Fall 1995, in C & O at Waterloo.
We read the book on Nonlinear Programming by Dimitri P. Bertsekas.

FAQ (frequently asked questions) on nonlinear programming.

Convex Optimization is a textbook by Stephen Boyd and Lieven Vandenberghe.

The CUTEr constrained and unconstrained testing environment.

ADIFOR: Automatic Differentiation of Fortran Codes.
ADIFOR is a tool for the automatic differentiation of Fortran 77 programs.

Last Modified:  Thursday 18 March 2010