Optimization Methods in Mathematical Modeling of Technological Processes (Mathematical Engineering)

✍ Scribed by Alena Vagaská, Miroslav Gombár, Anton Panda

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 181
• Category: Library

✦ Synopsis

This book focuses on selected methods of applied mathematics that are aimed at mathematical optimization, with an emphasis on their application in engineering practice. It delves into the current mathematical modeling of processes and systems, with a specific focus on the optimization modeling of technological processes. The authors discuss suitable linear, convex, and nonlinear optimization methods for solving problems in engineering practice. Real-world examples and data are used to numerically illustrate the implementation of these methods, utilizing the popular MATLAB software system and its extension to convex optimization. The book covers a wide range of topics, including mathematical modeling, linear programming, convex programming, and nonlinear programming, all with an engineering optimization perspective. It serves as a comprehensive guide for engineers, researchers, and students interested in the practical application of optimization methods in engineering.

✦ Table of Contents

Acknowledgments
Introduction
Aims of the Monograph
Contents
About the Authors
Abbreviations
1 Optimization in Historical Context
1.1 The Birth of Optimization as a Scientific Discipline
1.2 From Traditional to Modern Optimization Methods
References
2 Optimization
2.1 Mathematical Foundations of Optimization
2.1.1 Minimum of a Function
2.1.2 Gradient and Hessian
2.1.3 Definiteness and Semidefiniteness of a Matrix
2.1.4 Stationary Point
2.1.5 Convexity
2.1.6 Descent Direction
2.1.7 Convergence Rate
2.2 Formulation of an Optimization Problem
2.3 Classification of Optimization Problems
2.3.1 Linear Programming (LP)
2.3.2 Quadratic Programming (QP)
2.3.3 Nonlinear Programming (NP)
2.4 Optimality Conditions
2.5 Engineering Optimization (Process Optimization)
References
3 Optimization Methods in General
3.1 Classification of Optimization Methods
3.1.1 One-Dimensional Minimization Methods
3.1.2 Methods for Minimization a Function of n Variables
3.2 Testing of Optimization Algorithms
3.3 Stochastic Optimization Algorithms
References
4 Selected Methods of Multidimensional Optimization
4.1 Selected Methods of Nonlinear Programming
4.1.1 Nelder-Mead Simplex Method
4.1.2 Cauchy Steepest Descent Method
4.1.3 Newton’s Method
4.1.4 Quasi-Newton Methods—BFGS
4.2 Selected Methods of Linear Programming
4.2.1 Simplex Method
4.2.2 Interior Point Methods for Linear Programming
4.3 Simulated Annealing (SA)
References
5 Optimization of Technological Processes
5.1 Technological Processes Control—Optimal Decision Making
5.2 Formulation of Optimization Problem
5.3 Optimality Criterion
5.4 Mathematical Model
5.5 Perturbation Analysis
5.6 Selection of Optimization Method and Calculation Procedure
5.7 Demonstration of Optimal Decision Making Using Linear Programming
References
6 Application of Mathematical Programming Methods in Optimization of Cutting Conditions in Machining Processes
6.1 Selection of Optimal Cutting Parameters
6.2 Optimal Tool Life
6.3 Application of Mathematical Programming to Set Optimal Cutting Parameters
6.4 Constraint Conditions in Machining
6.4.1 Mathematical Formulation of Constraint Conditions in Turning
6.5 Mathematical Formulation of the Objective Function in Turning
6.6 Preparation for the Optimization Procedure of Cutting Conditions in Turning
6.7 Optimization Problem in Turning—Demonstration of Linear Programming Application
6.8 Solving the Optimization Problem Using MATLAB
References
7 Application of Nonlinear Programming Methods in Optimization of Surface Treatment Processes
7.1 Application of Nonlinear Programming to Optimize the Zincing Process
7.1.1 Galvanizing Process Analysis
7.1.2 Experimental Part—Galvanizing
7.1.3 Results of Experiment—Mathematical Model Creation
7.1.4 Optimization of the Galvanizing Process in MATLAB
7.2 Application of Nonlinear Programming to Optimize the Process of Anodic Aluminium Oxidation
7.2.1 Experimental Part—Anodic Aluminium Oxidation
7.2.2 Results of the Experiment—Mathematical Modelling
7.2.3 Optimization of Anodic Aluminium Oxidation Process in MATLAB
7.2.4 Discussion of the Results of Mathematical Modelling and Optimization of the Anodic Aluminium Oxidation Process
References
8 Conclusion
References