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2022 | Book

Basic Concepts, Lagrangian Methods and Linear Programming Problems Read chapter Read first chapter

Concise Guide to Optimization Models and Methods

A Problem-Based Test Prep for Students

Author: Xian Wen Ng

Publisher: Springer International Publishing

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This concise text contains the most commonly-encountered examination problems in the topic of Optimization Models and Methods, an important module in engineering and other disciplines where there exists an increasing need to operate optimally and sustainably under constraints, such as tighter resource availability, environmental consideration, and cost pressures. This book is comprehensive in coverage as it includes a diverse spectrum of problems from numerical open-ended questions that probe creative thinking to the relation of concepts to realistic settings. The book adopts many examples of design scenarios as context for curating sample problems. This will help students relate desktop problem-solving to tackling real-world problems. Succinct yet rigorous, with over a 100 pages of problems and corresponding worked solutions presented in detail, the book is ideal for students of engineering, applied science, and market analysis.

Table of Contents

Frontmatter
Basic Concepts, Lagrangian Methods and Linear Programming Problems
Abstract
This chapter builds a strong foundation in the understanding of the basic concepts and first principles behind how optimization works through problem formulation, and touches on the necessary conditions for minimization and maximization problems and what they mean. The concept of the Lagrangian method is introduced with detailed examples of its application. This chapter also includes examples of simple optimization problems involving only linear functions, which will provide beginner practice in problem formulation.
Xian Wen Ng
Non-linear Programming Problems with Constraints and Euler’s Methods
Abstract
This chapter introduces non-linear problems which require the consideration of various constraints in problem formulation. The worked solutions provided will guide students through problem solving techniques and train their ability to interpret complicated systems and systematically cast them into a concise set of objectives and parameters. The problems in this chapter include more rigorous methodologies such as discretization schemes, and Euler’s methods that would set the stage for more complex problems that require computer solvers.
Xian Wen Ng
Complex Optimization Problems
Abstract
This chapter rounds up the book by consolidating the concepts and techniques covered in prior chapters, and trains the student’s ability to apply these ideas to solving more challenging problems. The problems in this chapter mimic real-life scenarios, such as production planning for an industrial plant, or transportation route optimization for a logistics company, all having a desired objective (e.g. maximum profit or minimum cost) that is subject to specific constraints. In this topic, the student will gain exposure to problem types, and appreciate how the results of optimization allow key decisions to be made that would substantially drive better performance and outcomes.
Xian Wen Ng
Backmatter
Metadata
Title
Concise Guide to Optimization Models and Methods
Author
Xian Wen Ng
Copyright Year
2022
Electronic ISBN
978-3-030-84417-2
Print ISBN
978-3-030-84416-5
DOI
https://doi.org/10.1007/978-3-030-84417-2

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