Design Of Parallel Optimization Algorithm And Software And Port Of Numerical Software

Optimization has broad application in engineering, science, and management. Many of these applications either have large numbers of variables or require expensive function evaluations. These factors contribute to the need for more intensive computation than traditional architectures can support. High performance computing has provided powerful tools for solving these problems with a degree of practicability and efficiency that would otherwise be impossible.Optimization problems take different forms arising from the motivating applications. They can be linear or nonlinear, constrained or unconstrained, and local or global. The variety of optimization problems means that quite different parallel algorithms may be required and quite different architectures may be appropriate.The new computational technologies are having a very strong influence on numerical optimization. Many researchers have been stimulated by the need to either conform the existing numerical techniques to the new parallel architectures or to devise completely new parallel solution approaches. Two different trends, well representative for most of the current research activities, can be identified. Firstly, there is an attempt to encapsulate parallel linear algebra software and algorithms into optimization codes, and secondly, there is an effort to devise new parallel solution strategies in global optimization, either for specific or generalpurpose problems, motivated by the large size and the combinatorial nature of them.According to Schabel. bringing parallel computing into nonlinear optimization can be mainly done through the following three levels of parallelization:· parallelization of the function and/or the derivative evaluation in the algorithm;· parallelization of the linear algebra kernels:· modifications of the basic algorithms which increase the degree of intrinsic parallelism, for instance, by performing multiple function and /or derivative evaluations.For the different law between parallel computing and sequential computing, it should be taken into account that the nature of parallel algorithms and the properties of the problems while parallel algorithms are studied especially for large scale optimization problems. It is found that 60-70% of the time is spent in evaluating the line search step during solving the problems. If the progress is made in this process, much time can be saved, which is significantly important in solving large scale optimization problems. In this dissertation, we presented the global convergence properties of nonlinear conjugate gradient (NCG) methods without line search (NLS) and with strong Wolfe conditions, Goldstein inexact line search. NLS-NCG is an algorithm whose line search step length is determined by a formula instead of line search. It is particularly suitable for those large scale optimization problems that spend much time on line search step length.The Toolkit for Advanced Optimization (TAO) focuses on the development of algorithms and software for the solution of large-scale optimization problems on high-performance architectures. Areas of interest include nonlinear least squares, unconstrained and bound-constrained optimization, and general nonlinear optimization. TAO design philosophy uses object-oriented techniques of data and state encapsulation, abstract classes, and limited inheritance to create a flexible optimization toolkit. It has the common characteristics of the general softwarepackage, high performance, easy compiling and installing. And the C/Fortran compilers are supported. Because TAO is not welldeveloped so far. we add several solvers to TAO. such as cg.dyl, cg_dy2 and cg_nls_fr. From the numerical experiment, the new solvers cg_dy2 and cg_nls_fr has better parallel performance than the others. At the same time, we solved, by TAO, one problem from atmospheric sciences, nonlinear fastest growing perturbation and the first kind of predictability. The lines of parallel code are much fewer than those of the sequential. In addition, we can save much more time and solve the problem...