Optimization theory and algorithm
Introduction
This book is compiled by Professor Baolin Chen on the basis of many years of practice. The book includes linear programming simplex method, duality theory, sensitivity analysis, transportation problem, interior point algorithm , Non-linear programming KKT conditions, unconstrained optimization methods, constrained optimization methods, integer programming and dynamic programming. This book contains a large number of classic and recent algorithms, with a relatively systematic theoretical analysis, which is relatively practical; theorems The proof of and the derivation of the algorithm are mainly based on mathematical analysis and linear algebra, which is relatively simple and easy to learn. This book can be used as a teaching reference book for operations research courses, and can also be used as a reference for applied mathematics workers and engineering technicians.
Editor's recommendation
This book is composed of five parts: preliminary knowledge, linear programming, nonlinear programming, integer programming and dynamic programming. While maintaining the writing style of the first edition, some less commonly used algorithms are deleted, some chapters are rewritten, and linear programming with parameters, transportation problems, linear programming path tracking methods, trust region methods, and quadratic planning path tracking methods are added. Method, integer programming, dynamic programming, etc. Compared with the first edition, the algorithms in the second edition are richer, and the theory is in-depth, reflecting to a certain extent the new developments in some branches of operations research from time to time.
Book Catalog
Chapter 1 Introduction
1.1 Brief Introduction of Subjects
1.2 Linear and Nonlinear Programming Problems
< p>*1.3 Several mathematical generalizations1.4 Convex sets and convex functions
Exercises
Chapter 2 Basic Properties of Linear Programming
2.1 Standard Form and Graphical Method
2.2 Basic Properties
Exercises
Chapter 3 Simplex Method
3.1 Principles of Simplex Method
3.2 Two-stage method and big M method
3.3 Degenerate case
3.4 Modified simplex method
*3.5 Variable bounded Situation
*3.6 Decomposition Algorithm
Exercises
Chapter 4 Duality Principle and Sensitivity Analysis
4.1 Duality Theory in Linear Programming< /p>
4.2 Dual simplex method
4.3 Original dual algorithm
4.4 Sensitivity analysis
*4.5 Linear programming with parameters
< p>ExercisesChapter 5 Transportation Problems
5.1 Mathematical Models and Fundamentals of Transportation Problems
5.2 Operation Method on the Table
5.3 Transportation problem of unbalanced production and sales
Exercises
Chapter 6 Interior Point Algorithm of Linear Programming
*6.1Karmarkar Algorithm
*6.2 Interior Point Method
6.3 Path Tracing Method
Chapter 7 Optimality Conditions
7.1 Extreme Value Conditions for Unconstrained Problems
7.2 Optimality conditions for constrained extreme value problems
*7.3 Dual and saddle point problems
Exercises
*Chapter 8 Algorithms
8.1 Algorithm concept
8.2 Algorithm convergence problem
Exercises
Chapter 9 One-dimensional search
9.1 One-dimensional search concept
9.2 Heuristic Method
9.3 Function Approximation Method
Exercises
Chapter 10 Optimization Method Using Derivatives
10.1 Steepest descent method
10.2 Newton method
10.3 Conjugate gradient method
10.4 Quasi-Newton method
10.5 Trust region method
10.6 Least Squares
Exercises
Chapter 11 Direct Methods of Unconstrained Optimization
11.1 Pattern Search Method
11.2 Rosenbrock Method
11.3 Simplex Search Method
11.4 Powell Method
Exercises
Chapter 12 Feasible Direction Method
12.1 Zoutendijk feasible direction method
12.2 Rosen gradient projection method
*12.3 Reduced gradient method
12.4 Frank? Wolfe method
< p>ExercisesChapter 13 Penalty Function Method
13.1 External Point Penalty Function Method
13.2 Internal Point Penalty Function Method
* 13.3 Multiplier method
Exercises
Chapter 14 Secondary Planning
14.1 Lagrange Method
14.2 Working Set Method
14.3 Lemke Method
14.4 Path Tracing Method
Exercises
*Chapter 15 Introduction to Integer Programming
15.1 Branch Determination Boundary method
15.2 cutting plane method
15.301 implicit number method for planning
15.4 assignment problem
exercises
Chapter 16 Introduction to Dynamic Programming
16.1 Some Basic Concepts of Dynamic Programming
16.2 Basic Theorems and Basic Equations of Dynamic Programming
16.3 Inverse Solution and Sequence Solution
16.4 The relationship between dynamic programming and static programming
16.5 Function iteration method
Exercises
References
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