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Users guide for SnadiOpt : a package adding automatic differentiation to Snopt.

Description: SnadiOpt is a package that supports the use of the automatic differentiation package ADIFOR with the optimization package Snopt. Snopt is a general-purpose system for solving optimization problems with many variables and constraints. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for large-scale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. The method used by Snopt requires the first derivatives of the objective and constraint functions to be available. The SnadiOpt package allows users to avoid the time-consuming and error-prone process of evaluating and coding these derivatives. Given Fortran code for evaluating only the values of the objective and constraints, SnadiOpt automatically generates the code for evaluating the derivatives and builds the relevant Snopt input files and sparse data structures.
Date: June 21, 2001
Creator: Gertz, E. M.; Gill, P. E. & Muetherig, J.
Partner: UNT Libraries Government Documents Department

User's guide for SOL/QPSOL: a Fortran package for quadratic programming

Description: This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.
Date: July 1, 1983
Creator: Gill, P.E.; Murray, W.; Saunders, M.A. & Wright, M.H.
Partner: UNT Libraries Government Documents Department

New approaches to linear and nonlinear programming

Description: This program involves study of theoretical properties and computational performance of algorithms that solve linear and nonlinear programs. Emphasis is placed on algorithms to solve large problems, especially in the energy area. E.g., the safe, efficient distribution of electricity and the identification of the state of an electrical network are both large-scale nonlinearly constrained optimization problems. Other applications include optimal trajectory calculations and optimal structural design.
Date: February 1, 1993
Creator: Murray, W.; Saunders, M.A. (Stanford Univ., CA (United States). Dept. of Operations Research) & Gill, P.E. (San Diego State Univ., CA (United States). Dept. of Mathematics)
Partner: UNT Libraries Government Documents Department

Optimization and geophysical inverse problems

Description: A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the ...
Date: October 1, 2000
Creator: Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F. et al.
Partner: UNT Libraries Government Documents Department

Computing modified Newton directions using a partial Cholesky factorization

Description: The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step.
Date: March 1, 1993
Creator: Forsgren, A. (Royal Inst. of Tech., Stockholm (Sweden). Dept. of Mathematics); Gill, P.E. (California Univ., San Diego, La Jolla, CA (United States)) & Murray, W. (Stanford Univ., CA (United States). Systems Optimization Lab.)
Partner: UNT Libraries Government Documents Department