Читать книгу Linear and Convex Optimization - Michael H. Veatch - Страница 2
Table of Contents
Оглавление1 Cover
2 Linear and Convex Optimization
4 Preface
6 1 Introduction to Optimization Modeling 1.1 Who Uses Optimization? 1.2 Sending Aid to a Disaster 1.3 Optimization Terminology 1.4 Classes of Mathematical Programs
7 2 Linear Programming Models 2.1 Resource Allocation 2.2 Purchasing and Blending 2.3 Workforce Scheduling 2.4 Multiperiod Problems 2.5 Modeling Constraints 2.6 Network Flow
8 3 Linear Programming Formulations 3.1 Changing Form 3.2 Linearization of Piecewise Linear Functions 3.3 Dynamic Programming
9 4 Integer Programming Models 4.1 Quantitative Variables and Fixed Costs 4.2 Set Covering 4.3 Logical Constraints and Piecewise Linear Functions 4.4 Additional Applications 4.5 Traveling Salesperson and Cutting Stock Problems
10 5 Iterative Search Algorithms 5.1 Iterative Search and Constructive Algorithms 5.2 Improving Directions and Optimality 5.3 Computational Complexity and Correctness
11 6 Convexity 6.1 Convex Sets 6.2 Convex and Concave Functions
12 7 Geometry and Algebra of LPs 7.1 Extreme Points and Basic Feasible Solutions 7.2 Optimality of Extreme Points 7.3 Linear Programs in Canonical Form 7.4 Optimality Conditions 7.5 Optimality for General Polyhedra
13 8 Duality Theory 8.1 Dual of a Linear Program 8.2 Duality Theorems 8.3 Complementary Slackness 8.4 Lagrangian Duality 8.5 Farkas' Lemma and Optimality
14 9 Simplex Method 9.1 Simplex Method From a Known Feasible Solution 9.2 Degeneracy and Correctness 9.3 Finding an Initial Feasible Solution 9.4 Computational Strategies and Speed
15 10 Sensitivity Analysis 10.1 Graphical Sensitivity Analysis 10.2 Shadow Prices and Reduced Costs 10.3 Economic Interpretation of the Dual
16 11 Algorithmic Applications of Duality 11.1 Dual Simplex Method 11.2 Network Simplex Method 11.3 Primal‐Dual Interior Point Method
17 12 Integer Programming Theory 12.1 Linear Programming Relaxations 12.2 Strong Formulations 12.3 Unimodular Matrices
18 13 Integer Programming Algorithms 13.1 Branch and Bound Methods 13.2 Cutting Plane Methods
19 14 Convex Programming: Optimality Conditions 14.1 KKT Optimality Conditions 14.2 Lagrangian Duality
20 15 Convex Programming: Algorithms 15.1 Convex Optimization Models 15.2 Separable Programs 15.3 Unconstrained Optimization 15.4 Quadratic Programming 15.5 Primal‐dual Interior Point Method
21 A Linear Algebra and Calculus Review A.1 Sets and Other Notation A.2 Matrix and Vector Notation A.3 Matrix Operations A.4 Matrix Inverses A.5 Systems of Linear Equations A.6 Linear Independence and Rank A.7 Quadratic Forms and Eigenvalues A.8 Derivatives and Convexity
22 Bibliography
23 Index
