[Classic Book] Practical mathematics optimization: Basic optimization theory and gradient -based algorithm

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This book provides extensive mathematical optimization curriculum tools for senior undergraduates and graduate students in mathematics, engineering, computer science and other applied sciences.

This book provides extensive mathematical optimization curriculum tools for senior undergraduates and graduate students in mathematics, engineering, computer science and other applied sciences. The basic principles of optimization are introduced, and the gradient -based numerical optimization strategies and algorithms are introduced, which can be used to solve the problem of smooth and noise discontinuous optimization. It is also noticed that the difficulty of the function value and multiple minimum values ​​are often unnecessary to suppress the use of gradient -based methods. This second edition introduces the further improvement of gradient optimization strategies to deal with the discontinuity in the target function. The new chapter discusses the structure of the proxy model, as well as the new gradient solution strategy and the use of Python numerical optimization. A special Python module is provided by electronic (through Springerlink), which makes the new algorithm in the text easy to access and apply directly. The value examples and exercises include the student programs that encourage advanced levels of graduate students, implement it, and reflect numerical surveys. Through in -depth understanding of conceptual materials, students, scientists and engineers will be able to develop systems and scientific digital research skills.

https://link.springer.com/book/10.1007/978-319-77586-9-9

Mathematical optimization is usually called non -linear planning, mathematical planning or numerical optimization. In more general terms, mathematics optimization can be described as the best solution to determine the problem of mathematical definition problems. These problems may be a model of physical reality or manufacturing and management systems. In the first case, the solutions are usually corresponding to the minimum energy configuration of the general structure of the general structure from the molecular to the suspension bridge, so they are interested in science and engineering. In the second case, business and financial considerations that have the importance of economic and industrial economic and industrial business have begun to play, and demand decisions, such as ensuring the maximum profit or the lowest cost.

The focus of this book is almost fully concentrated in gradient -based methods. There are two reasons. (i) The author believes that the theme of the introduction of mathematics optimization is best to complete through classic gradient -based methods. Optimization and other evolution methods, the author believes that in many cases, these search methods are too expensive and not feasible in computing. The existence of numerical noise and multiple minimum values ​​is not suitable for the use of gradient -based methods, and the only solution in this case is to use the above non -gradient search technology, which is not necessarily correct. According to the author's experience, through the wise use of gradient -based methods, it can solve the problem with numerical noise and multiple minimum values, and only requires a small part of the calculation cost of search technology such as genetic algorithms. In this context, Chapter 6 discusses the new gradient -based method developed by the first author and the pure gradient method developed by Chapter 8. This is particularly important. The presentation of the materials is not strict, but the hope is correct. It should provide necessary information to allow scientists and engineers to choose appropriate optimization algorithms and successfully apply them to their respective interests.

Directory content:

Basic Optimization theory

INTRODUCTION

LINE Search Descent Methods for Unconstrained Minimization

Standard Methods for Constrained Optimization

BASIC Example Proplems

SOME BASIC OPTIMATION Theorems

Gradient-based algorithms

New Gradient-Based Trajectory and Approximation Methods

Surrogate Models

Gradient-only solution strategies

Practical Computational Optimization Use Python

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