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Contents Chapter 1: Introduction and Problem Formulation
1.1 Introduction
1.2 Some Examples
1.2.1 The Diet Problem
1.2.2 The Standard Linear Programming Problem
1.2.3 The Transportation Problem
1.3 Infinite Dimensional Optimization Problems
1.3.1 An Example of a Problem of Calculus of Variations
1.3.2 Problem Formulation
1.3.3 The Fundamental Theorem of Calculus of Variations
1.3.4 Approximate Solution of Problems in Calculus of Variations
1.4 An Example of the Approximate Technique
1.5.1 An Optimal Control Problem: Rocket Launching
1.5.2 An Optimal Control Problem: Highway Construction
Chapter 2: Basic Theorems and Complex Analysis
2.1 Basic Theorems of Optimization: First Order Necessary Conditions
2.2 Basic Theorems of Optimization: Second Order Necessary Conditions
2.3 An Introduction to Convex Analysis
2.3 An Introduction to Convex Analysis (Continued)
2.4 Generalized Projection Theorem
2.5 Convex and Concave Functions
2.6 Properties of Differentiable Convex Functions
2.7 Twice Differentiable Convex and Concave Functions
2.8 Minima and Maxima of Convex Functions
Chapter 3: Unconstrained Optimization
3.1 Introduction to Unconstrained Optimization
3.2 An Example of One Dimensional Search
3.3 The Concept of an Algorithm
3.4 The Solution Set Concept and Convergence of Algorithms
3.5 Composition of Mappings
3.6 Convergence of Algorithms with Composite Maps
3.7 The Method of Steepest Descent
3.8 The Quadratic Case
3.9 Convergence Rate of the Steepest Descent Method
3.10 Quadratic Steepest Descent Method: Case Study
3.11 Line Search Without Using Derivatives
3.12 Sequential Search
Chapter 4: Constrained Optimization
Chapter 5: Evolutionary Computation Techniques
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