#optimization
90. Operations Research, Mathematical Programming
This volume studies decision-making under constraints using mathematical models. It integrates optimization, stochastic models, and algorithmic methods. Part I. Foundations Chapter 1. Optimization Models 1.1 Decision variables 1.2 Objective functions 1.3 Constraints 1.4 Feasible regions 1.5 Examples Chapter 2. Linear Programming 2.1 Standard form 2.2 Feasible solutions 2.3 Geometry of solutions 2.4 Applications 2.5 Examples Chapter 3. Duality 3.1 Dual problems 3.2 Weak and strong duality 3.3 Complementary slackness 3.4...
49. Calculus of Variations and Optimal Control; Optimization
This volume studies optimization of functionals and systems. It connects analysis, geometry, control theory, and computation. Part I. Foundations of Optimization Chapter 1. Optimization Problems 1.1 Definitions and examples 1.2 Objective functions and constraints 1.3 Local and global optima 1.4 Existence of solutions 1.5 Examples Chapter 2. Convexity 2.1 Convex sets 2.2 Convex functions 2.3 Properties 2.4 Jensen’s inequality 2.5 Applications Chapter 3. Optimality Conditions 3.1 First-order conditions 3.2 Second-order...