基本説明
Contents: Introduction; Linear Programming; Nonlinear Programming; Discrete Optimization; Optimization Under Uncertainty; Multi-objective Optimization; Optimal Control and Dynamic Optimization; and more.
Full Description
Most of the books in optimization are devoted to details of one or two aspects of the subject e.g. linear and nonlinear programming, stochastic programming, optimal control, stochastic dynamic programming, mixed integer programming, heuristic methods, or multi-objective programming etc., or are written for a specific discipline. The wide scope of optimization mandates extensive interaction between various disciplines in the development of the methods and algorithms, and in their fruitful application to real world problems. This book presents a discipline independent view of optimization for scientists, researchers, and analysts in various fields. It provides them opportunities to identify and apply algorithms, methods and tools from the diverse areas of optimization to their own field without getting into too much detail about the underlying theories. This work is for researchers in various fields as well as undergraduate and graduate students in engineering, management science, and decision science.
Contents
1 IntroductionFreedom Analysis; Objective Function, Constraints, and Feasible Region; Numerical Optimization; Types of Optimization Problems; Summary. 2 Linear Programming: The Simplex Method; Infeasible Solution; Unbounded Solution; Multiple Solutions; Sensitivity Analysis; Other Methods; Hazardous Waste Blending Problem as an LP; Summary. 3 Nonlinear Programming: Convex and Concave Functions; Unconstrained NLP; Necessary and Sufficient Conditions, and Constrained NLP; Sensitivity Analysis; Numerical Methods; Hazardous Waste Blending - An NLP; Summary. 4 Discrete Optimization: Tree and Network Representation; Branch and Bound for IP; Numerical Methods for IP, MILP, and MINLP; Probabilistic Methods; Hazardous Waste Blending - A Combinatorial Problem; Summary. 5 Optimization Under Uncertainty: Types of Problems and Generalized Representation; Chance Constrained Programming Method; L-shaped Decomposition Method; Uncertainty Analysis and Sampling; Stochastic Annealing - An Efficient Algorithm for Combinatorial Optimization under Uncertainty; Hazardous Waste Blending under Uncertainty; Summary. 6 Multi-objective Optimization; Nondominated Set; Solution Methods; Hazardous Waste Blending and Value of Research - An MOP; Summary. 7 Optimal control And Dynamic Optimization: Calculus of Variations; Maximum Principle; Dynamic Programming; Stochastic Dynamic Programming; Reversal of Blending - Optimizing a Separation Process; Summary.
