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E-raamat: Optimizations and Programming: Linear, Non-linear, Dynamic, Stochastic and Applications with Matlab

(Universities at INSA-RouenNormandie, France), (Hassan Premier University, Morocco)
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  • Ilmumisaeg: 27-Apr-2021
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119818267
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Optimizations and Programming: Linear, Non-linear, Dynamic, Stochastic and Applications with MatlabSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 27-Apr-2021
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119818267
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This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them.

The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more.

Preface xi
Part 1 Programmation
1(126)
Chapter 1 Linear Programming
3(38)
1.1 Introduction
3(1)
1.2 Definitions
3(2)
1.3 Geometry of the linear program
5(1)
1.3.1 Polyhedra
5(1)
1.3.2 Extreme points and vertices
6(1)
1.4 Graphical solving of a linear program
6(3)
1.5 Simplex algorithm
9(6)
1.5.1 Basic solutions and basic feasible solutions
9(1)
1.5.2 Simplex tableau
10(1)
1.5.3 Change of feasible basis
11(3)
1.5.4 Existence and uniqueness of an optimal solution
14(1)
1.6 Initialization of the simplex algorithm
15(7)
1.6.1 Big M method
15(2)
1.6.2 Auxiliary program or Phase I
17(3)
1.6.3 Degeneracy and cycling
20(1)
1.6.4 Geometric structure of realizable solutions
21(1)
1.7 Interior-point algorithm
22(1)
1.8 Duality
23(4)
1.8.1 Duality theorem
25(2)
1.9 Relaxation
27(2)
1.9.1 Lagrangian relaxation
27(2)
1.10 Postoptimal analysis
29(5)
1.10.1 Effect of modifying 6
31(1)
1.10.2 Effect of modifying c
32(2)
1.11 Application to an inventory problem
34(2)
1.11.1 Optimal solution
34(1)
1.11.2 Sensitivity to variation in stock
35(1)
1.11.3 Dual problem of the competitor
36(1)
1.12 Using Matlab
36(5)
Chapter 2 Integer Programming
41(24)
2.1 Introduction
41(1)
2.2 Solving methods
41(8)
2.2.1 Branch-and-bound method
42(2)
2.2.2 The branch-and-cut method
44(5)
2.3 Binary programming
49(8)
2.3.1 Knapsack problem
49(1)
2.3.2 Investment problem
50(7)
2.4 Decomposition principle
57(5)
2.4.1 Benders decomposition
58(4)
2.5 Using Matlab
62(3)
Chapter 3 Dynamic Programming
65(28)
3.1 Introduction
65(1)
3.2 Solving strategy
66(2)
3.3 Discrete DP
68(15)
3.3.1 Bellman's equation and the principle of optimality
68(2)
3.3.2 Approach of the method
70(1)
3.3.3 A few examples of DP
70(3)
3.3.4 Solving an LP
73(1)
3.3.5 Shortest path problem
74(5)
3.3.6 Knapsack problem
79(2)
3.3.7 Stock management problem
81(2)
3.4 Continuous DP
83(2)
3.4.1 Hamilton-Jacobi equation
84(1)
3.4.2 Application to a consumption-savings model
84(1)
3.5 Stochastic DP
85(6)
3.5.1 Decision-chance process
85(1)
3.5.2 Solving method
86(1)
3.5.3 Application to a contract problem
86(1)
3.5.4 Optimal binary search tree
87(4)
3.6 Using Matlab
91(2)
Chapter 4 Stochastic Programming
93(34)
4.1 Introduction
93(1)
4.2 Presentation of the problem
94(1)
4.3 Optimal feedback in an open loop
94(1)
4.4 Stochastic linear programming
95(1)
4.4.1 Models with probability thresholds on the constraints
96(1)
4.5 Stochastic linear programs with recourse
96(4)
4.5.1 L-shaped method
97(2)
4.5.2 Multicut L-shaped method
99(1)
4.5.3 Interior linearization method
100(1)
4.6 Nonlinear stochastic programming
100(7)
4.6.1 Approaches to two-step problems with recourse
100(1)
4.6.2 Regularized decomposition method
101(1)
4.6.3 Methods based on the Lagrangian
101(2)
4.6.4 Frank-Wolfe method for problems with simple recourse
103(2)
4.6.5 Approximation by sampling average: Monte Carlo method
105(1)
4.6.6 Stochastic gradient method
106(1)
4.7 Stochastic dynamic programming
107(4)
4.7.1 Markov decision process
108(1)
4.7.2 Scenario tree
109(2)
4.8 Application to the reliability of mechanical systems
111(10)
4.8.1 Position and modeling of the reliability problem
113(8)
4.9 Using Matlab
121(6)
Part 2 Optimization
127(102)
Chapter 5 Combinatorial Optimization
129(32)
5.1 Introduction
129(2)
5.2 Symmetric TSP
131(9)
5.2.1 Historical overview
132(2)
5.2.2 Solving methods
134(6)
5.3 Asymmetric traveling salesman problem
140(8)
5.3.1 Variants of the ATSP
140(2)
5.3.2 Mathematical formulations
142(2)
5.3.3 Methods for solving the ATSP
144(4)
5.4 Vehicle routing problem
148(8)
5.4.1 Definition
148(1)
5.4.2 Fields of application
149(1)
5.4.3 Parameters of the VRP
150(1)
5.4.4 Variants of the VRP
151(2)
5.4.5 Mathematical formulation of the VRP
153(2)
5.4.6 Algorithmic complexity
155(1)
5.5 Selective routing problem
156(2)
5.5.1 Problems similar to the VRP
157(1)
5.5.2 Mathematical formulation
157(1)
5.6 Using Matlab
158(3)
Chapter 6 Unconstrained Nonlinear Programming
161(32)
6.1 Introduction
161(1)
6.2 Mathematical formulation
161(1)
6.2.1 Existence and uniqueness results
162(1)
6.3 Optimality conditions
162(1)
6.4 Quadratic problems
163(1)
6.4.1 Gradient method with optimal step size
163(1)
6.4.2 Conjugate gradient method
164(1)
6.5 Newton's algorithm
164(1)
6.6 Methods of descent and linear search
165(6)
6.6.1 Presentation of methods of descent
165(2)
6.6.2 Method of greatest slope
167(1)
6.6.3 Acceptable step size
168(1)
6.6.4 Linear search
169(1)
6.6.5 Newton's method with linear search
170(1)
6.7 Quasi-Newton methods
171(2)
6.7.1 DFP and BFGS methods
172(1)
6.8 Relaxation method
173(2)
6.9 Gradient method
175(1)
6.10 Least squares problem
176(5)
6.10.1 Gauss-Newton method
176(2)
6.10.2 Levenberg-Marquardt algorithm
178(1)
6.10.3 Kalman filter
179(2)
6.11 Direct search methods
181(2)
6.11.1 Nelder-Mead algorithm
181(2)
6.11.2 Torczon method
183(1)
6.12 Application to an identification problem
183(2)
6.13 Using Matlab
185(8)
6.13.1 The fminsearch function
187(1)
6.13.2 The fminunc function
188(2)
6.13.3 Relaxation method
190(3)
Chapter 7 Constrained Nonlinear Optimization
193(36)
7.1 Introduction
193(1)
7.2 Mathematical formulation
193(1)
7.3 Lagrange multipliers
194(1)
7.4 Optimization with inequality constraints
195(6)
7.4.1 First-order conditions of optimality
195(2)
7.4.2 Presentation of saddle points
197(1)
7.4.3 Saddle point and optimization
198(3)
7.4.4 Convex case
201(1)
7.5 Constrained minimization algorithms
201(5)
7.5.1 Relaxation method
202(1)
7.5.2 Projection method
202(2)
7.5.3 Exterior penalty method
204(1)
7.5.4 Uzawa's algorithm
205(1)
7.6 Newton algorithms: SQP method
206(4)
7.6.1 Equality constraints
207(2)
7.6.2 Inequality constraints
209(1)
7.7 Application to structure optimization
210(7)
7.8 Using Matlab
217(12)
7.8.1 The fmincon function
219(2)
7.8.2 The fminbnd function 220
7.8.3 Penalty method
221(8)
Appendices 229(2)
Appendix 1 Reminders from Linear Algebra 231(10)
Appendix 2 Reminders about functions from Rn into R 241(4)
Appendix 3 Optimization Toolbox 245(4)
Appendix 4 Software 249(4)
References 253(8)
Index 261
Abdelkhalak El Hami is Full Professor of Universities at INSA-RouenNormandie, France. He is the author/co-author of several books and is responsible for the Chair of mechanics at the Conservatoire National des Arts et Métiers in Normandy, as well as for several European pedagogical projects. He is a specialist in problems of optimization and reliability in multi-physical systems.

Bouchaïb Radi is Professor at the Faculty of Science and Technology at Hassan Premier University, Morocco. He is a specialist in numerical optimization methods and system reliability.
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