19 Matching Results

Search Results

Advanced search parameters have been applied.

Global methods for nonlinear complementarity problems

Description: Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations approach, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only requires the solution of systems of linear equations. Convergence to a solution of the nonlinear complementarity problem is guaranteed under reasonable regularity assumptions. The converge rate is Q-linear, Q-superlinear, or Q-quadratic, depending on the tolerances used to solve the subproblems.
Date: April 1, 1994
Creator: More, J.J.
Partner: UNT Libraries Government Documents Department

Automatic differentiation tools in optimization software.

Description: The authors discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our discussion centers on the computation of the gradient and Hessian matrix for partially separable functions and shows that the gradient and Hessian matrix can be computed with guaranteed bounds in time and memory requirements.
Date: January 15, 2001
Creator: More, J. J.
Partner: UNT Libraries Government Documents Department

Design of optimization software

Description: The MINPACK project aims to develop a systematized collection of quality optimization software. The package MINPACK-1 solves systems of nonlinear equations and nonlinear least-squares problems. First this package is outlined, and then some of the design principles employed during the development of MINPACK-1 are discussed. These concepts are robustness, scale invariance, interface routines, and reverse communication. (RWR)
Date: January 1, 1979
Creator: More, J J
Partner: UNT Libraries Government Documents Department

Global smoothing and continuation for large-scale molecular optimization

Description: We discuss the formulation of optimization problems that arise in the study of distance geometry, ionic systems, and molecular clusters. We show that continuation techniques based on global smoothing are applicable to these molecular optimization problems, and we outline the issues that must be resolved in the solution of large-scale molecular optimization problems.
Date: October 1995
Creator: More, J. J. & Wu, Zhijun
Partner: UNT Libraries Government Documents Department

Benchmarking optimization software with COPS.

Description: The COPS test set provides a modest selection of difficult nonlinearly constrained optimization problems from applications in optimal design, fluid dynamics, parameter estimation, and optimal control. In this report we describe version 2.0 of the COPS problems. The formulation and discretization of the original problems have been streamlined and improved. We have also added new problems. The presentation of COPS follows the original report, but the description of the problems has been streamlined. For each problem we discuss the formulation of the problem and the structural data in Table 0.1 on the formulation. The aim of presenting this data is to provide an approximate idea of the size and sparsity of the problem. We also include the results of computational experiments with the LANCELOT, LOQO, MINOS, and SNOPT solvers. These computational experiments differ from the original results in that we have deleted problems that were considered to be too easy. Moreover, in the current version of the computational experiments, each problem is tested with four variations. An important difference between this report and the original report is that the tables that present the computational experiments are generated automatically from the testing script. This is explained in more detail in the report.
Date: January 8, 2001
Creator: Dolan, E.D. & More, J.J.
Partner: UNT Libraries Government Documents Department

Smoothing of mixed complementarity problems

Description: The authors introduce a smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. The main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions to the mixed complementarity problem. The analysis is applicable to a wide variety of algorithms suitable for large-scale mixed complementarity problems.
Date: September 1, 1995
Creator: Gabriel, S.A. & More, J.J.
Partner: UNT Libraries Government Documents Department

Smoothing techniques for macromolecular global optimization

Description: We study global optimization problems that arise in macromolecular modeling, and the solution of these problems via continuation and smoothing. Our results unify and extend the theory associated with the use of the Gaussian transform for smoothing. We show that the, Gaussian transform can be viewed as a special case of a generalized transform and that these generalized transforms share many of the properties of the Gaussian transform. We also show that the smoothing behavior of the generalized transform can be studied in terms of the Fourier transform and that these results indicate that the Gaussian transform has superior smoothing properties.
Date: September 1, 1995
Creator: More, J.J. & Wu, Zhijun
Partner: UNT Libraries Government Documents Department

Implementation guide for MINPACK-1. [Package of Fortran subprograms for solution of systems of nonlinear equations]

Description: MINPACK-1 is a package of Fortran subprograms for the numerical solution of systems of nonlinear equations and nonlinear least-squares problems. This report describes how to implement the package from the tape on which it is transmitted. 3 tables.
Date: July 1, 1980
Creator: Garbow, B.S.; Hillstrom, K.E. & More, J.J.
Partner: UNT Libraries Government Documents Department

Newton's method

Description: Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach. The other aim is to present some of the recent developments in the optimization field which are related to Newton's method. In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method.
Date: February 1, 1982
Creator: More, J. J. & Sorensen, D. C.
Partner: UNT Libraries Government Documents Department

Optimization environments and the NEOS server

Description: The authors are interested in the development of problem-solving environments that simplify the formulation of optimization problems, and the access to computational resources. Once the problem has been formulated, the first step in solving an optimization problem in a typical computational environment is to identify and obtain the appropriate piece of optimization software. Once the software has been installed and tested in the local environment, the user must read the documentation and write code to define the optimization problem in the manner required by the software. Typically, Fortran or C code must be written to define the problem, compute function values and derivatives, and specify sparsity patterns. Finally, the user must debug, compile, link, and execute the code. The Network-Enabled Optimization System (NEOS) is an Internet-based service for optimization providing information, software, and problem-solving services for optimization. The main components of NEOS are the NEOS Guide and the NEOS Server. The current version of the NEOS Server is described in Section 2. The authors emphasize nonlinear optimization problems, but NEOS does handle linear and nonlinearly constrained optimization problems, and solvers for optimization problems subject to integer variables are being added. In Section 4 the authors begin to explore possible extensions to the NEOS Server by discussing the addition of solvers for global optimization problems. Section 5 discusses how a remote procedure call (RPC) interface to NEOS addresses some of the limitations of NEOS in the areas of security and usability. The detailed implementation of such an interface raises a number of questions, such as exactly how the RPC is implemented, what security or authentication approaches are used, and what techniques are used to improve the efficiency of the communication. They outline some of the issues in network computing that arise from the emerging style of computing used by NEOS.
Date: March 1, 1997
Creator: Gropp, W. & More, J.J.
Partner: UNT Libraries Government Documents Department

Global continuation for distance geometry problems

Description: Distance geometry problems arise in the interpretation of NMR data and in the determination of protein structure. The authors formulate the distance geometry problem as a global minimization problem with special structure, and show the global smoothing techniques and a continuation approach for global optimization can be used to determine solutions of distance geometry problems with a nearly 100% probability of success.
Date: March 1, 1995
Creator: More, J.J. & Wu, Zhijun
Partner: UNT Libraries Government Documents Department

Remote access to mathematical software.

Description: The network-oriented application services paradigm is becoming increasingly common for scientific computing. The popularity of this approach can be attributed to the numerous advantages to both user and developer provided by network-enabled mathematical software. The burden of installing and maintaining complex systems is lifted from the user, while enabling developers to provide frequent updates without disrupting service. Access to software with similar functionality can be unified under the same interface. Remote servers can utilize potentially more powerful computing resources than may be available locally. We discuss some of the application services developed by the Mathematics and Computer Science Division at Argonne National Laboratory, including the Network Enabled Optimization System (NEOS) Server and the Automatic Differentiation of C (ADIC) Server, as well as preliminary work on Web access to the Portable Extensible Toolkit for Scientific Computing (PETSc). We also provide a brief survey of related work.
Date: August 22, 2001
Creator: Dolan, E.; Hovland, P.; More, J.; Norris, B. & Smith, B.
Partner: UNT Libraries Government Documents Department

COPS: Large-scale nonlinearly constrained optimization problems

Description: The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.
Date: February 10, 2000
Creator: Bondarenko, A.S.; Bortz, D.M. & More, J.J.
Partner: UNT Libraries Government Documents Department

Benchmarking optimization software with COPS 3.0.

Description: The authors describe version 3.0 of the COPS set of nonlinearly constrained optimization problems. They have added new problems, as well as streamlined and improved most of the problems. They also provide a comparison of the FILTER, KNITRO, LOQO, MINOS, and SNOPT solvers on these problems.
Date: May 24, 2004
Creator: Dolan, E. D.; More, J. J. & Munson, T. S.
Partner: UNT Libraries Government Documents Department

TAO users manual.

Description: The Toolkit for Advanced Optimization (TAO) focuses on the design and implementation of component-based optimization software for the solution of large-scale optimization applications on high-performance architectures. Their approach is motivated by the scattered support for parallel computations and lack of reuse of linear algebra software in currently available optimization software. The TAO design allows the reuse of toolkits that provide lower-level support (parallel sparse matrix data structures, preconditioners, solvers), and thus they are able to build on top of these toolkits instead of having to redevelop code. The advantages in terms of efficiency and development time are significant. The TAO design philosophy uses object-oriented techniques of data and state encapsulation, abstract classes, and limited inheritance to create a flexible optimization toolkit. This chapter provides a short introduction to the design philosophy by describing the objectives in TAO and the importance of this design. Since a major concern in the TAO project is the performance and scalability of optimization algorithms on large problems, they also present some performance results.
Date: December 2, 2003
Creator: Benson, S.; McInnes, L. C.; More, J. J. & Sarich, J.
Partner: UNT Libraries Government Documents Department

The MINPACK-2 test problem collection

Description: Optimization software has often been developed without any specific application in mind. This generic approach has worked well in many cases, but as we seek the solution of larger and more complex optimization problems on high-performance computers, the development of optimization software should take into account specific optimization problems that arise in a wide range of applications. This observation was the motivation for the development of the MINPACK-2 test problem collection. Each of the problems in this collection comes from a real application and is representative of other commonly encountered problems. There are problems from such diverse fields as fluid dynamics, medicine, elasticity, combustion, molecular conformation, nondestructive testing, chemical kinetics, lubrication, and superconductivity.
Date: June 1992
Creator: Averick, B. M.; Carter, R. G.; Xue, Guo-Liang & More, J. J.
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