TAO users manual.
Published 2 December 2003Open access
Sara Benson, Lois Curfman McInnes, Jorge J. Morè, J. Sarich
Citations53
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
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.
Keywords
Computer ScienceMathematics
The Computer JournalA Simplex Method for Function Minimization
28,856 Citations1965J. A. Nelder, R. Mead
A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Proceedings of the National Academy of SciencesEquilibrium points in <i>n</i> -person games
7,320 Citations1950John F. Nash
A concept of an n -person game in which each player has a finite set of pure strategies and in which a definite set of payments to the n players corresponds to each n -tuple ofpure strategies, one strategy being taken for each player.
Society for Industrial and Applied Mathematics eBooksTrust Region Methods
2,901 Citations2000Andrew R. Conn, Nicholas I. M. Gould +1 more
This chapter discusses Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations and Nonlinear Fitting, and some of the methods used in this chapter dealt with these systems.
Computers & Mathematics with ApplicationsUsing MPI: Portable parallel programming with the message-passing interface
2,897 Citations1995
Thank you very much for downloading using mpi portable parallel programming with the message passing interface for reading a good book with a cup of coffee in the afternoon, instead they are facing with some malicious bugs inside their laptop.
MPI: A Message-Passing Interface Standard
2,709 Citations1994Message P Forum
This document contains all the technical features proposed for the interface and the goal of the Message Passing Interface, simply stated, is to develop a widely used standard for writing message-passing programs.
Birkhäuser Boston eBooksEfficient Management of Parallelism in Object-Oriented Numerical Software Libraries
1,984 Citations1997Satish Balay, William Gropp +2 more
The concepts discussed are appropriate for all scalable computing systems and provide many of the data structures and numerical kernels required for the scalable solution of PDEs, offering performance portability.
Mathematical ProgrammingA nonsmooth version of Newton's method
1,480 Citations1993Liqun Qi, Jie Sun
It is shown that the gradient function of the augmented Lagrangian forC2-nonlinear programming is semismooth, and the extended Newton's method can be used in the augmentedlagrangian method for solving nonlinear programs.
SIAM Journal on Numerical AnalysisA Nonmonotone Line Search Technique for Newton’s Method
1,134 Citations1986Luigi Grippo, F. Lampariello +1 more
A nonmonotone steplength selection rule for Newton's method is proposed, which can be viewed as a generalization of Armijo’s rule, which indicates that the proposed technique may allow a considerable saving both in the number of line searches and in thenumber of function evaluations.
SIAM ReviewEngineering and Economic Applications of Complementarity Problems
1,065 Citations1997Michael C. Ferris, Jong‐Shi Pang
The goal of this documentation is to summarize the essential applications of the nonlinear complementarity problem known to date, to provide a basis for the continued research on the non linear complementarityproblem, and to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Minima of Functions of Several Variables with Inequalities as Side Conditions
854 Citations2013William Karush
SIAM Journal on Control and OptimizationSemismooth and Semiconvex Functions in Constrained Optimization
829 Citations1977Robert Mifflin
Mathematics of Operations ResearchConvergence Analysis of Some Algorithms for Solving Nonsmooth Equations
734 Citations1993Liqun Qi
Convergence analysis of some algorithms for solving systems of nonlinear equations defined by locally Lipschitzian functions and a hybrid method, which is both globally convergent in the sense of finding a stationary point of the norm function of the system and locally quadratically convergent, is presented.
Mathematical ProgrammingA semismooth equation approach to the solution of nonlinear complementarity problems
376 Citations1996Tecla De Luca, Francisco Facchinei +1 more
The recent extension of Newton's method to semismooth systems of equations and the fact that the natural merit function associated to the equation reformulation is continuously differentiable are exploited to develop an algorithm whose global and quadratic convergence properties can be established under very mild assumptions.
SIAM Journal on OptimizationOn the Solution of Large Quadratic Programming Problems with Bound Constraints
338 Citations1991Jorge J. Morè, Gerardo Toraldo
It is proved that for strictly convex problems the algorithm converges to the solution, and that if the solution is nondegenerate, then the algorithm terminates at the solution in a finite number of steps.
SIAM Journal on OptimizationNewton's Method for Large Bound-Constrained Optimization Problems
315 Citations1999Chih‐Jen Lin, Jorge J. Morè
A trust region version of Newton's method for bound-constrained problems that holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints.
SIAM Journal on Applied MathematicsNonlinear Programs with Positively Bounded Jacobians
171 Citations1966Richaard W. Cottle
The Journal of Computational FinanceOption pricing and linear complementarity
101 Citations1998Jacqueline Huang, Jong‐Shi Pang
INFORMS journal on computingThe Semismooth Algorithm for Large Scale Complementarity Problems
69 Citations2001Todd Munson, Francisco Facchinei +3 more
The semismooth algorithm has the potential to meet both reliability and scalability requirements and is described in detail as a sophisticated implementation that scales well to very large problems.
BlockSolve95 users manual: Scalable library software for the parallel solution of sparse linear systems
32 Citations1995Mark T. Jones, Paul E. Plassmann
This report gives detailed instructions on the use of BlockSolve95 and descriptions of a number of program examples that can be used as templates for application programs.