Optimization: Foundations and Applications

ISBN-13: 9780471351696 / Angielski / Miękka / 1999 / 676 str.

Ronald E. Miller

Opis

A thorough and highly accessible resource for analysts in a broad range of social sciences.

Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods.

Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root-finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:

• More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics
  
• Classic results mixed with modern numerical methods to aid users of computer programs
  
• Extensive appendices containing mathematical details important for a thorough understanding of the topic
  
  With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences.
  
  An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

Recenzje

The author′s extensive teaching experience is reflected in his upbeat, relaxed writing style and preesntation. (Short Book Reviews, V21, No1, April 2001)

"...accessible to people who have neither formal mathematical training nor any background in optimization...this text could be useful for an introductory class on optimization..." (SIAM Review, Vol. 43, No. 3)

Spis treści

FOUNDATIONS: LINEAR METHODS.

Matrix Algebra.

Systems of Linear Equations.

FOUNDATIONS: NONLINEAR METHODS.

Unconstrained Maximization and Minimization.

Constrained Maximization and Minimization.

APPLICATIONS: ITERATIVE METHODS FOR NONLINEAR PROBLEMS.

Solving Nonlinear Equations.

Solving Unconstrained Maximization and Minimization Problems.

APPLICATIONS: CONSTRAINED OPTIMIZATION IN LINEAR MODELS.

Linear Programming: Fundamentals.

Linear Programming: Extensions.

Linear Programming: Interior Point Methods.

APPLICATIONS: CONSTRAINED OPTIMIZATION IN NONLINEAR MODELS.

Nonlinear Programming: Fundamentals.

Nonlinear Programming: Duality and Computational Methods.

Problems.

References.

O autorze

RONALD E. MILLER, PhD, is professor emeritus of regional science at the University of Pennsylvania.

Blurb

A thorough and highly accessible resource for analysts in a broad range of social sciences.

Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award–winning educator Ronald E. Miller provides detailed coverage of both classical, calculus–based approaches and newer, computer–based iterative methods.

Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to discuss applications, including iterative methods for root–finding and for unconstrained maximization, approaches to the inequality constrained linear programming problem, and the complexities of inequality constrained maximization and minimization in nonlinear problems. Other important features include:

• More than 200 geometric interpretations of algebraic results, emphasizing the intuitive appeal of mathematics
• Classic results mixed with modern numerical methods to aid users of computer programs
• Extensive appendices containing mathematical details important for a thorough understanding of the topic

With special emphasis on questions most frequently asked by those encountering this material for the first time, Optimization: Foundations and Applications is an extremely useful resource for professionals in such areas as mathematics, engineering, economics and business, regional science, geography, sociology, political science, management and decision sciences, public policy analysis, and numerous other social sciences.