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.

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.