Table of contents of optimization theories and methods, optimization theories and methods

"Optimization Theory and Method" is a book published by the National Defense Industry Press on June 1, 2008, and the author is Fu Yingding. The contents of this book include optimization basics, linear programming, dual linear programming, unconstrained optimization methods, constrained optimization methods, direction acceleration methods for direct search, multi-objective optimization, dynamic programming, etc.

This book is based on the original textbook "Optimization Theory and Method". This revision listened to the opinions of teachers and students who used this book, deleted some complicated mathematical derivations, added some more mature algorithms, and corrected some arrangement errors, so as to make the content and system more complete and convenient for self-study and teaching.

This book has the characteristics of appropriate materials, moderate difficulty, attention to ideas, concise algorithms, and easy self-study and teaching, and is suitable for engineering graduate students, senior engineering undergraduates and students majoring in applied mathematics.

This book systematically introduces the optimization theories and methods commonly used in mechanical engineering, which is divided into four chapters: linear programming and integer programming, nonlinear programming, intelligent optimization methods, variational method and dynamic programming, with a total of 15 chapters. Part 1 covers the fundamentals of optimization, linear programming, and integer programming.

After introducing the basic contents of optimization such as optimization variables, objective functions, constraints and mathematical modeling, the basic forerunner principle and the most commonly used simplex method for linear programming are discussed, and then two solutions for integer linear programming are given. In the second part, nonlinear programming includes the mathematical analysis basis of nonlinear programming, one-dimensional optimization methods, unconstrained sliding-based multi-dimensional optimization methods, and constrained nonlinear programming methods.

The intelligent optimization methods in the third paper include heuristic search method, hopfield neural network optimization method, simulated annealing method and even-field annealing method, genetic algorithm, etc. In the fourth part, the variational method, the principle of maximum (small) value, and dynamic programming are introduced. Each chapter is equipped with exercises.

This book can be used as a teaching and scientific research reference book for graduate students and teachers of optimization theory and method courses of the first-level discipline of mechanical engineering in colleges and universities, as well as a teaching book for other related majors, as well as a reference book for engineering technology and scientific researchers engaged in production planning, optimization design and optimal control.

1. Unconstrained optimization.

2. Optimization with constraints.

That is, the study is of the function minimization problem. (Example) Burial 1, select the initial point.

3. Determine the step size factor so that the value of the objective function has a meaningful decrease.

4. Let , if a certain termination condition is satisfied, then stop the response and iterate to obtain the optimal solution, otherwise repeat step (2).

1. Consider quadratic forms.

Question: Why quadratic? ）

2. Visualization of quadratic forms.

Curl roll in the above formula.

3. Apply the gradient method to find out the direction of descent.

Question 1: Is it best to choose the direction along the direction of gradient descent? ——the steepest descent

Question 2: What are the properties of the best?

4. For quadratic types, there are.

5. Find out the step size of the descent.

2) Approximate step size (not exact).

6. Common optimization methods.

1) Fastest descent method.

2) Newton's method.

3) Conjugate gradient method.

4) Quasi-Newtonian method.

This book is compiled by Professor Chen Baolin on the basis of many years of practice. The book includes linear programming simplex methods, dual theory, sensitivity analysis, transportation problems, interior point algorithms, and nonlinear programmingt-condition, unconstrained optimization methods, constrained optimization methods, integer programming, dynamic programming, etc.

This book contains a large number of classic and recent algorithms, with relatively systematic theoretical analysis and strong practicability. The proof of theorems and the derivation of algorithms are mainly based on mathematical analysis and linear algebra, which are relatively simple and easy to learn. This book can be used as a teaching reference for operations research courses, as well as for mathematicians and engineering technicians.