Optimizations and Programming

Optimizations and Programming
Авторы книги: id книги: 2052338     Оценка: 0.0     Голосов: 0     Отзывы, комментарии: 0 17001,8 руб.     (183,62$) Читать книгу Купить и скачать книгу Купить бумажную книгу Электронная книга Жанр: Техническая литература Правообладатель и/или издательство: John Wiley & Sons Limited Дата добавления в каталог КнигаЛит: ISBN: 9781119818267 Скачать фрагмент в формате   fb2   fb2.zip Возрастное ограничение: 0+ Оглавление Отрывок из книги

Реклама. ООО «ЛитРес», ИНН: 7719571260.

Описание книги

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.

Оглавление

Abdelkhalak El Hami. Optimizations and Programming

Table of Contents

List of Tables

List of Illustrations

Guide

Pages

Optimizations and Programming. Linear, Nonlinear, Dynamic, Stochastic and Applications with Matlab

Preface

Acknowledgments

1. Linear Programming. 1.1. Introduction

1.2. Definitions

Terminology

1.3. Geometry of the linear program. 1.3.1. Polyhedra

1.3.2. Extreme points and vertices

1.4. Graphical solving of a linear program

1.5. Simplex algorithm

1.5.1. Basic solutions and basic feasible solutions

1.5.2. Simplex tableau

General case

1.5.3. Change of feasible basis

Calculating the new tableau

1.5.4. Existence and uniqueness of an optimal solution

1.6. Initialization of the simplex algorithm

1.6.1. Big M method

1.6.2. Auxiliary program or Phase I

1.6.3. Degeneracy and cycling

1.6.4. Geometric structure of realizable solutions

1.7. Interior-point algorithm

1.8. Duality

1.8.1. Duality theorem

Application

1.9. Relaxation

1.9.1. Lagrangian relaxation

1.10. Postoptimal analysis

1.10.1. Effect of modifying b

1.10.2. Effect of modifying c

Case of a non-basic variable

1.11. Application to an inventory problem

1.11.1. Optimal solution

1.11.2. Sensitivity to variation in stock

1.11.3. Dual problem of the competitor

1.12. Using Matlab

2. Integer Programming. 2.1. Introduction

2.2. Solving methods

2.2.1. Branch-and-bound method

2.2.2. The branch-and-cut method

2.3. Binary programming

2.3.1. Knapsack problem

2.3.2. Investment problem

2.4. Decomposition principle

2.4.1. Benders decomposition

2.5. Using Matlab

3. Dynamic Programming. 3.1. Introduction

3.2. Solving strategy

3.3. Discrete DP

3.3.1. Bellman’s equation and the principle of optimality

3.3.2. Approach of the method

3.3.3. A few examples of DP. 3.3.3.1. Example of a mailman

3.3.4. Solving an LP

3.3.5. Shortest path problem

3.3.6. Knapsack problem

3.3.7. Stock management problem

3.4. Continuous DP

3.4.1. Hamilton–Jacobi equation

3.4.2. Application to a consumption-savings model

3.5. Stochastic DP

3.5.1. Decision-chance process

3.5.2. Solving method

3.5.3. Application to a contract problem

3.5.4. Optimal binary search tree

3.5.4.1. Formulation of the problem

3.5.4.2. Formulation of the solution

3.6. Using Matlab

4. Stochastic Programming. 4.1. Introduction

4.2. Presentation of the problem

4.3. Optimal feedback in an open loop

4.4. Stochastic linear programming

4.4.1. Models with probability thresholds on the constraints

4.5. Stochastic linear programs with recourse

4.5.1. L-shaped method

4.5.2. Multicut L-shaped method

4.5.3. Interior linearization method

4.6. Nonlinear stochastic programming. 4.6.1. Approaches to two-step problems with recourse

4.6.2. Regularized decomposition method

4.6.3. Methods based on the Lagrangian

4.6.4. Frank–Wolfe method for problems with simple recourse

4.6.5. Approximation by sampling average: Monte Carlo method

4.6.6. Stochastic gradient method

4.7. Stochastic dynamic programming

4.7.1. Markov decision process

4.7.2. Scenario tree

4.8. Application to the reliability of mechanical systems

4.8.1. Position and modeling of the reliability problem

4.8.1.1. Deterministic mechanical model

4.8.1.2. Randomness and probabilistic modeling

4.8.1.3. Failure modes of a structure

4.8.1.4. Failure probability of a structure

4.8.1.5. Hasofer and Lind index

4.8.1.6. FORM method

4.9. Using Matlab

5. Combinatorial Optimization. 5.1. Introduction

5.2. Symmetric TSP

5.2.1. Historical overview

5.2.2. Solving methods. 5.2.2.1. Exact methods

5.2.2.2. Approximate methods

5.3. Asymmetric traveling salesman problem

5.3.1. Variants of the ATSP

5.3.2. Mathematical formulations

5.3.2.1. DFJ formulation

5.3.2.2. MTZ formulation

5.3.2.3. Desrochers–Laporte formulation

5.3.3. Methods for solving the ATSP

5.3.3.1. Branch-and-bound method

5.3.3.2. Cutting-plane method

5.3.3.3. Branch-and-cut method

5.4. Vehicle routing problem. 5.4.1. Definition

5.4.2. Fields of application

5.4.3. Parameters of the VRP

5.4.4. Variants of the VRP

5.4.5. Mathematical formulation of the VRP

Formulation

5.4.6. Algorithmic complexity

5.5. Selective routing problem

5.5.1. Problems similar to the VRP

5.5.2. Mathematical formulation

5.6. Using Matlab

6. Unconstrained Nonlinear Programming. 6.1. Introduction

6.2. Mathematical formulation

6.2.1. Existence and uniqueness results

6.3. Optimality conditions

6.4. Quadratic problems

6.4.1. Gradient method with optimal step size

6.4.2. Conjugate gradient method

6.5. Newton’s algorithm

6.6. Methods of descent and linear search. 6.6.1. Presentation of methods of descent

6.6.2. Method of greatest slope

6.6.3. Acceptable step size

6.6.4. Linear search

6.6.5. Newton’s method with linear search

6.7. Quasi-Newton methods

6.7.1. DFP and BFGS methods

6.8. Relaxation method

6.9. Gradient method

6.10. Least squares problem

6.10.1. Gauss–Newton method

6.10.2. Levenberg–Marquardt algorithm

6.10.3. Kalman filter

6.11. Direct search methods

6.11.1. Nelder–Mead algorithm

6.11.2. Torczon method

6.12. Application to an identification problem

6.13. Using Matlab

6.13.1. The fminsearch function

6.13.2. The fminunc function

6.13.3. Relaxation method

7. Constrained Nonlinear Optimization. 7.1. Introduction

7.2. Mathematical formulation

7.3. Lagrange multipliers

7.4. Optimization with inequality constraints

7.4.1. First-order conditions of optimality. 7.4.1.1. Lagrange conditions

7.4.1.2. Karush–Kuhn–Tucker conditions

7.4.2. Presentation of saddle points

7.4.3. Saddle point and optimization

7.4.4. Convex case

7.5. Constrained minimization algorithms

7.5.1. Relaxation method

7.5.2. Projection method

7.5.3. Exterior penalty method

7.5.4. Uzawa’s algorithm

7.6. Newton algorithms: SQP method

7.6.1. Equality constraints

7.6.2. Inequality constraints

7.7. Application to structure optimization

7.8. Using Matlab

7.8.1. The fmincon function

7.8.2. The fminbnd function

7.8.3. Penalty method

Appendix 1. Reminders from Linear Algebra

A1.1. Vector space. A1.1.1. General definitions

A1.1.2. Free families, generating families and bases

A1.2. Linear mappings

A1.3. Matrices

A1.3.1. Operations on matrices

Properties

A1.3.2. Change of basis matrices

A1.3.3. Matrix notation

A1.4. Determinants

Properties

Properties

A1.5. Scalar product

A1.6. Vector norm

Appendix 2. Reminders about functions from ℝn into ℝ

A2.1. Differentiability

A2.2. Convexity

A2.3. Quadratic function

Appendix 3. Optimization Toolbox. A3.1. Introduction

A3.2. Various functions

A3.3. Matlab’s optimization application

Appendix 4. Software. A4.1. Autonomous and multipurpose optimization software

A4.2. Packages for specific classes of problems

A4.3. Optimization software for design

A4.4. Solvers for stochastic optimization

References

Index

WILEY END USER LICENSE AGREEMENT

Отрывок из книги

Digital Sciences Set

.....

More recently, Bland [BLA 77] suggested modifying the rules for choosing the change of basis. Bland’s rule proceeds as follows:

Earlier, when we solved linear programs graphically, the optimal solutions were on the boundary of the convex set of realizable solutions. If there was a unique optimal solution, it was an extreme point.

.....

Добавление нового отзыва

Комментарий Поле, отмеченное звёздочкой  — обязательно к заполнению

Отзывы и комментарии читателей

Нет рецензий. Будьте первым, кто напишет рецензию на книгу Optimizations and Programming
Подняться наверх