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E-raamat: Optimization and Approximation

  • Formaat: PDF+DRM
  • Sari: La Matematica per il 3+2 108
  • Ilmumisaeg: 07-Sep-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319648439
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Optimization and ApproximationSuurem pilt
  • Formaat: PDF+DRM
  • Sari: La Matematica per il 3+2 108
  • Ilmumisaeg: 07-Sep-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319648439
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This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Arvustused

This book, consisting of eight chapters, provides an introduction to optimization aimed at engineering and science students. ... This book is equally suitable to those without prior knowledge in the field as well as those already familiar with the key concepts as a useful reference. The book concludes with a very useful appendix containing hints or full solutions to the exercises presented throughout the book. (Efstratios Rappos, zbMATH 1375.90002, 2018)

1 Overview
1(10)
1.1 Importance of Optimization Problems
1(1)
1.2 Optimization
2(3)
1.2.1 Unconstrained Optimization and Critical Points
2(1)
1.2.2 Constrained Optimization
3(1)
1.2.3 Variational Problems
4(1)
1.2.4 Optimal Control Problems
4(1)
1.3 Approximation
5(2)
1.4 Structure and Use of the Book
7(4)
Part I Mathematical Programming
2 Linear Programming
11(22)
2.1 Some Motivating Examples
11(3)
2.2 Structure of Linear Programming Problems
14(5)
2.3 Sensitivity and Duality
19(3)
2.4 A Final Clarifying Example
22(3)
2.5 Final Remarks
25(1)
2.6 Exercises
26(7)
2.6.1 Exercises to Support the Main Concepts
26(3)
2.6.2 Practice Exercises
29(1)
2.6.3 Case Studies
30(3)
3 Nonlinear Programming
33(30)
3.1 Some Motivating Examples
33(4)
3.2 Structure of Non-linear Programming Problems
37(1)
3.3 Optimality Conditions
38(9)
3.4 Convexity
47(5)
3.5 Duality
52(3)
3.6 Final Remarks
55(1)
3.7 Exercises
56(7)
3.7.1 Exercises to Support the Main Concepts
56(2)
3.7.2 Practice Exercises
58(3)
3.7.3 Case Studies
61(2)
4 Numerical Approximation
63(26)
4.1 Practical Numerical Algorithms for Unconstrained Minimization
64(3)
4.1.1 The Direction
64(1)
4.1.2 Step Size
65(2)
4.2 A Perspective for Constrained Problems Based on Unconstrained Minimization
67(6)
4.2.1 The Algorithm for Several Constraints
70(2)
4.2.2 An Important Issue for the Implementation
72(1)
4.3 Some Selected Examples
73(5)
4.4 Final Remarks
78(1)
4.5 Exercises
78(11)
4.5.1 Exercises to Support the Main Concepts
78(3)
4.5.2 Computer Exercises
81(2)
4.5.3 Case Studies
83(2)
References
85(4)
Part II Variational Problems
5 Basic Theory for Variational Problems
89(26)
5.1 Some Motivating Examples
89(5)
5.2 Existence of Optimal Solutions
94(2)
5.3 Optimality Conditions Under Smoothness
96(5)
5.4 Constraints
101(3)
5.5 Final Remarks
104(1)
5.6 Exercises
104(11)
5.6.1 Exercises to Support the Main Concepts
104(4)
5.6.2 Practice Exercises
108(3)
5.6.3 Case Studies
111(4)
6 Numerical Approximation of Variational Problems
115(24)
6.1 Importance of the Numerical Treatment
115(1)
6.2 Approximation Under Smoothness
115(4)
6.2.1 The Descent Direction
116(3)
6.3 Approximation Under Constraints
119(2)
6.4 Some Examples
121(7)
6.5 The Algorithm in Pseudocode Form
128(2)
6.6 Exercises
130(9)
6.6.1 Exercises to Support the Main Concepts
130(1)
6.6.2 Computer Exercises
131(2)
6.6.3 Case Studies
133(1)
References
134(5)
Part III Optimal Control
7 Basic Facts About Optimal Control
139(28)
7.1 Some Motivating Examples
139(3)
7.2 An Easy Existence Result
142(2)
7.3 Optimality Conditions
144(6)
7.4 Pontryaguin's Principle
150(6)
7.5 Other Important Constraints
156(3)
7.6 Sufficiency of Optimality Conditions
159(1)
7.7 Final Remarks
160(1)
7.8 Exercises
160(7)
7.8.1 Exercises to Support the Main Concepts
160(2)
7.8.2 Practice Exercises
162(2)
7.8.3 Case Studies
164(3)
8 Numerical Approximation of Basic Optimal Control Problems, and Dynamic Programming
167(26)
8.1 Introduction
167(1)
8.2 Reduction to Variational Problems
168(3)
8.3 A Much More Demanding Situation
171(4)
8.4 Dynamic Programming
175(9)
8.5 Final Remarks
184(1)
8.6 Exercises
185(8)
8.6.1 Exercises to Support the Main Concepts
185(1)
8.6.2 Computer Exercises
185(2)
8.6.3 Case Studies
187(2)
References
189(4)
Part IV Appendix
9 Hints and Solutions to Exercises
193
9.1
Chapter 2
193(7)
9.1.1 Exercises to Support the Main Concepts
193(3)
9.1.2 Practice Exercises
196(1)
9.1.3 Case Studies
197(3)
9.2
Chapter 3
200(8)
9.2.1 Exercises to Support the Main Concepts
200(2)
9.2.2 Practice Exercises
202(4)
9.2.3 Case Studies
206(2)
9.3
Chapter 4
208(6)
9.3.1 Exercises to Support the Main Concepts
208(1)
9.3.2 Computer Exercises
209(2)
9.3.3 Case Studies
211(3)
9.4
Chapter 5
214(10)
9.4.1 Exercises to Support the Main Concepts
214(3)
9.4.2 Practice Exercises
217(3)
9.4.3 Case Studies
220(4)
9.5
Chapter 6
224(7)
9.5.1 Exercises to Support the Main Concepts
224(1)
9.5.2 Computer Exercises
225(4)
9.5.3 Case Studies
229(2)
9.6
Chapter 7
231(10)
9.6.1 Exercises to Support the Main Concepts
231(5)
9.6.2 Practice Exercises
236(2)
9.6.3 Case Studies
238(3)
9.7
Chapter 8
241
9.7.1 Exercises to Support the Main Concepts
241(1)
9.7.2 Computer Exercises
242(3)
9.7.3 Case Studies
245
Pablo Pedregal  studied Mathematics at U. Complutense (1986) and received his PhD degree from the University of Minnesota at the end of 1989, under the guidance of D. Kinderlehrer. In 1990 he became associate professor at U. Complutense. During the academic year 1994-95 he moved to the young U. de Castilla-La Mancha, and in 1997 he won a full professorship. His field of interest focuses on variational techniques applied to optimization in a broad sense, including, but not limited to, calculus of variations -especially vector, non convex problems, optimal design in continuous media, optimal control, etc, and more recently he has explored variational ideas in areas like controllability, inverse problems, PDEs, and dynamical systems. Since his doctorate, he has regularly traveled to research centers in the USA and Europe. He has written more than one hundred research articles, and several specialized books.
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