Optimization Theory

A Concise Introduction

Nonfiction, Science & Nature, Mathematics, Linear Programming
Cover of the book Optimization Theory by Jiongmin Yong, World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jiongmin Yong ISBN: 9789813237667
Publisher: World Scientific Publishing Company Publication: May 10, 2018
Imprint: WSPC Language: English
Author: Jiongmin Yong
ISBN: 9789813237667
Publisher: World Scientific Publishing Company
Publication: May 10, 2018
Imprint: WSPC
Language: English

Mathematically, most of the interesting optimization problems can be formulated to optimize some objective function, subject to some equality and/or inequality constraints. This book introduces some classical and basic results of optimization theory, including nonlinear programming with Lagrange multiplier method, the Karush–Kuhn–Tucker method, Fritz John's method, problems with convex or quasi-convex constraints, and linear programming with geometric method and simplex method.

A slim book such as this which touches on major aspects of optimization theory will be very much needed for most readers. We present nonlinear programming, convex programming, and linear programming in a self-contained manner. This book is for a one-semester course for upper level undergraduate students or first/second year graduate students. It should also be useful for researchers working on many interdisciplinary areas other than optimization.

Contents:

  • Mathematical Preparation (including Basics of Euclidean Space, Linear Algebra, Limits, Continuity, and Differentiability of Functions)
  • Optimization Problems and Existence of Optimal Solutions
  • Necessary and Sufficient Conditions of Optimal Solutions (including Problems with No Constraint, with Equality Constraints, and with Equality and Inequality Constraints)
  • Problems with Convexity and Quasi-Convexity Conditions (including Convex Sets and Convex Functions, Optimization Problems with Convex and Quasi-Convex Constraints, Lagrange Duality)
  • Linear Programming (including Geometric Method, Simplex Method, Sensitivity Analysis, and Duality Theory)

Readership: Undergraduates; graduates and researchers interested in classical and basic optimization theory.
Key Features:

  • Based on the preparation material (standard calculus and linear algebra presented in the first chapter), the presentation of all the major results of optimization are self-contained
  • We use Ekeland's variational principle to prove Fritz John's optimality conditions. As far as the author's knowledge, this is new
  • The theoretic results and examples have been balanced. All the major theorems are companioned by its proof and some examples. This enables the readers who are not interested in the proofs to proceed to learn how to use the theorems from the examples
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Mathematically, most of the interesting optimization problems can be formulated to optimize some objective function, subject to some equality and/or inequality constraints. This book introduces some classical and basic results of optimization theory, including nonlinear programming with Lagrange multiplier method, the Karush–Kuhn–Tucker method, Fritz John's method, problems with convex or quasi-convex constraints, and linear programming with geometric method and simplex method.

A slim book such as this which touches on major aspects of optimization theory will be very much needed for most readers. We present nonlinear programming, convex programming, and linear programming in a self-contained manner. This book is for a one-semester course for upper level undergraduate students or first/second year graduate students. It should also be useful for researchers working on many interdisciplinary areas other than optimization.

Contents:

Readership: Undergraduates; graduates and researchers interested in classical and basic optimization theory.
Key Features:

More books from World Scientific Publishing Company

Cover of the book The Mathematics That Power Our World by Jiongmin Yong
Cover of the book Discrete Fractional Calculus by Jiongmin Yong
Cover of the book Structural Aspects of Protein Synthesis by Jiongmin Yong
Cover of the book Solution Manual for Quantum Mechanics by Jiongmin Yong
Cover of the book Energy from the Nucleus by Jiongmin Yong
Cover of the book Approximation of Set-Valued Functions by Jiongmin Yong
Cover of the book 2017 Annual Competitiveness Analysis and Impact of Exchange Rates on Foreign Direct Investment Inflows to Sub-National Economies of Indonesia by Jiongmin Yong
Cover of the book White Noise Analysis and Quantum Information by Jiongmin Yong
Cover of the book Gulf Politics and Economics in a Changing World by Jiongmin Yong
Cover of the book Computational Physics by Jiongmin Yong
Cover of the book Singapore Perspectives 2015 by Jiongmin Yong
Cover of the book Classical Mechanics by Jiongmin Yong
Cover of the book A Complexity Approach to Sustainability by Jiongmin Yong
Cover of the book Resilience and Resolve by Jiongmin Yong
Cover of the book Computational and Algorithmic Linear Algebra and n-Dimensional Geometry by Jiongmin Yong
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy