Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Two approaches are known for solving large-scale unconstrained optimization problems—the limited-memory quasi-Newton method (truncated Newton method) and the conjugate gradient method. This is the first book to detail conjugate gradient methods, showing their properties and convergence characteristics as well as their performance in solving large-scale unconstrained optimization problems and applications. Comparisons to the limited-memory and truncated Newton methods are also discussed. Topics studied in detail include: linear conjugate gradient methods, standard conjugate gradient methods, acceleration of conjugate gradient methods, hybrid, modifications of the standard scheme, memoryless BFGS preconditioned, and three-term. Other conjugate gradient methods with clustering the eigenvalues or with the minimization of the condition number of the iteration matrix, are also treated. For each method, the convergence analysis, the computational performances and the comparisons versus other conjugate gradient methods are given. The theory behind the conjugate gradient algorithms presented as a methodology is developed with a clear, rigorous, and friendly exposition; the reader will gain an understanding of their properties and their convergence and will learn to develop and prove the convergence of his/her own methods. Numerous numerical studies are supplied with comparisons and comments on the behavior of conjugate gradient algorithms for solving a collection of 800 unconstrained optimization problems of different structures and complexities with the number of variables in the range [1000,10000]. The book is addressed to all those interested in developing and using new advanced techniques for solving unconstrained optimization complex problems. Mathematical programming researchers, theoreticians and practitioners in operations research, practitioners in engineering and industry researchers, as well as graduate students in mathematics, Ph.D. and master students in mathematical programming, will find plenty of information and practical applications for solving large-scale unconstrained optimization problems and applications by conjugate gradient methods.

Conjugate gradient methods. --- Constrained optimization. --- Optimization, Constrained --- Mathematical optimization --- Gradient methods, Conjugate --- Approximation theory --- Equations --- Iterative methods (Mathematics) --- Numerical solutions --- Mathematical optimization. --- Mathematical models. --- Optimization. --- Mathematical Modeling and Industrial Mathematics. --- Models, Mathematical --- Simulation methods --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- System analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This up-to-date book is on algorithms for large-scale unconstrained and bound constrained optimization. Optimization techniques are shown from a conjugate gradient algorithm perspective. Large part of the book is devoted to preconditioned conjugate gradient algorithms. In particular memoryless and limited memory quasi-Newton algorithms are presented and numerically compared to standard conjugate gradient algorithms. The special attention is paid to the methods of shortest residuals developed by the author. Several effective optimization techniques based on these methods are presented. Because of the emphasis on practical methods, as well as rigorous mathematical treatment of their convergence analysis, the book is aimed at a wide audience. It can be used by researches in optimization, graduate students in operations research, engineering, mathematics and computer science. Practitioners can benefit from numerous numerical comparisons of professional optimization codes discussed in the book.

Algorithms. --- Conjugate gradient methods. --- Mathematical optimization. --- Conjugate gradient methods --- Algorithms --- Mathematical optimization --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Mathematical Theory --- Operations Research --- Algebra --- Calculus --- Algorism --- Gradient methods, Conjugate --- Mathematics. --- Operations research. --- Decision making. --- Calculus of variations. --- Quality control. --- Reliability. --- Industrial safety. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Quality Control, Reliability, Safety and Risk. --- Arithmetic --- Approximation theory --- Equations --- Iterative methods (Mathematics) --- Foundations --- Numerical solutions --- System safety. --- Operations Research/Decision Theory. --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Systems engineering --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Prevention --- Industrial accidents --- Industries --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Reliability (Engineering) --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Isoperimetrical problems --- Variations, Calculus of --- Decision making