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Synopsis: Classical Optimization Techniques. Optimization and Inequalities. Numerical Methods of Optimization. Linear Programming Techniques. Nonlinear Programming Techniques. Dynamic Programming Methods. Variational Methods. Stochastic Approximation Procedures. Optimization in Simulation. Optimization in Function Spaces. Classical Optimization Techniques: Preliminaries. Necessary and Sufficient Conditions for an Extremum. Constrained Optimization--Lagrange Multipliers. Statistical Applications. Optimization and Inequalities: Classical Inequalities. Matrix Inequalities. Applications. Numerical Methods of Optimization: Numerical Evaluation of Roots of Equations. Direct Search Methods. Gradient Methods. Convergence of Numerical Procedures. Nonlinear Regression and Other Statistical Algorithms. Linear Programming Techniques: Linear Programming Problem. Standard Form of the Linear Programming Problem. Simplex Method. Karmarkar's Algorithm. Zero-Sum TwoPerson Finite-Games and Linear Programming. Integer Programming. Statistical Applications. Nonlinear Programming Methods: Statistical Examples. Kuhn-Tucker Conditions. Quadratic Programming. Convex Programming. Applications. Statistical Control ofOptimization. Stochastic Programming. Geometric Programming. Dynamic Programming Methods: Regulation and Control. Functional Equation and Principles of Optimality. Dynamic Programming and Approximation. Patient Care through Dynamic Programming. Pontryagin Maximum Principle. Miscellaneous Applications. Variational Methods: Statistical Applications. Euler-Lagrange Equations. Neyman-Pearson Technique. Robust Statistics and Variational Methods. Penalized Maximum Likelihood Estimates. StochasticApproximation Procedures: Robbins-Monro Procedure. General Case. Kiefer-Wolfowitz Procedure. Applications. Stochastic Approximation and Filtering. Optimization in Simulation: Optimization Criteria. Optimality of Regression Experiments. ResponseSurface Methods. Miscellaneous Stochastic Methods. Application. Optimization in Function Spaces: Preliminaries. Optimization Results. Splines in Statistics. Chapter Exercises. Bibliography. Author Index. Subject Index.
Statistics help guide us to optimal decisions under uncertainty. A large variety of statistical problems are essentially solutions to optimization problems. The mathematical techniques of optimization are fundamentalto statistical theory and practice. In this book, Jagdish Rustagi provides full-spectrum coverage of these methods, ranging from classical optimization and Lagrange multipliers, to numerical techniques using gradients or direct search, to linear, nonlinear, and dynamic programming using the Kuhn-Tucker conditions or the Pontryagin maximal principle. Variational methods and optimization in function spaces are also discussed, as are stochastic optimization in simulation, including annealing methods.
The text features numerous applications, including:
Finding maximum likelihood estimates
Markov decision processes
Programming methods used to optimize monitoring of patients in hospitals
Derivation of the Neyman-Pearson lemma
The search for optimal designs
Simulation of a steel mill
Suitable as both a reference and a text, this book will be of interest to advanced undergraduate or beginning graduate students in statistics, operations research, management and engineering sciences, and related fields. Most of the material can be covered in one semester by students with a basic background in probability and statistics.
- Covers optimization from traditional methods to recent developments such as Karmarkars algorithm and simulated annealing
- Develops a wide range of statistical techniques in the unified context of optimization
- Discusses applications such as optimizing monitoring of patients and simulating steel mill operations
- Treats numerical methods and applications
- Includes exercises and references for each chapter
- Covers topics such as linear, nonlinear, and dynamic programming, variational methods, and stochastic optimization
Researchers, practitioners, and students in applied statistics and operations research; advanced undergraduate and graduate level courses in these areas
- No. of pages:
- © Academic Press 1994
- 25th April 1994
- Academic Press
- eBook ISBN:
"It is well written, nicely organized, with a high degree of mathematical accuracy...all coming together to make the material easily digestible." --Stergios B. Fotopoulos, Washington State University
"I enjoyed reading this book and strongly recommend it for its contribution to the field of statistics. I believe that it will have a positive impact on the content of optimization courses taught in both management and mathematical graduate programs." --Stergios B. Fotopoulos, Washington State University
The Ohio State University
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