Sold Out
Book Categories |
Foreword xi
Preface xiii
The study of optimization 1
Mathematics and practitioners 1
Applying optimization methods 3
Mathematical background 5
Variables and functions 5
Differentiation and integration of functions 6
Vectors 8
Definition of regions 10
Matrices 11
Permutations 12
Set notation 12
Definition of a network 13
Probability distributions 14
Optimization problems and methods 17
Basic components 17
Problem variables 17
Objective functions 18
Constraints 19
Equality constraints 19
Inequality constraints 20
Discrete constraints 21
Disjoint alternative regions 22
The general optimization problem 23
Global optima 23
Local optima 23
The search for the optimum 24
Optimization methods 25
Calculus and Lagrange multipliers 29
The achievement of thecalculus 29
Restrictions on the use of the calculus 30
Problems in one variable 31
Unconstrained problems in two or more variables 33
Equality constraints: Lagrange multipliers 35
Sufficient conditions for local maxima and minima 37
Proof of the Lagrange multiplier method 39
Linear programming 42
Linear functions 42
The standard form 43
Converting to the standard form 43
The ideas of the simplex method 45
The canonical form 47
Improving the basis 49
Transformation to the new canonical form 51
Summary of the procedure for a change of basis 51
Obtaining an initial solution 54
The simplex tableau 56
The revised simplex method 58
Difficulties in special cases 61
The fundamental theorem of linear programming 61
The convex space of feasible solutions 63
Optimization of non-linear functions 65
Non-linear optimization techniques 65
Local and global optima 66
Finding an initial feasible solution 67
Unconstrained problems: the failure of the calculus 69
Steepest descent for unconstrained problems 69
More advanced descent methods for unconstrained problems 72
Projected gradient methods for linear constraints 75
Created response surface techniques for general constraints 80
Direct search procedures 84
Separable programming 88
Approximation programming 91
The direction of steepest descent 95
Construction of the projection matrix 96
Convergence of the response surface technique 97
Dynamic programming 101
The aim of dynamic programming 101
Multi-stage decision processes 102
The dynamic programming method: forwards calculation 103
The backwards calculation 105
Network problems 106
Allocation of a single resource to a number of activities 108
Reliability problems 113
Computational comments 114
Allocation processes involving two types of resources or two constraints 116
Problems with two neighbouring stages related: backward calculations 118
A stochastic problem 119
Branch and bound methods 123
Solutions as tree searches 123
Rules for the branch and bound method 125
The three-machine scheduling problem 127
The knapsack problem 131
Integer programming 134
Computational considerations 138
Suboptimization 138
Permutation procedures 141
The need to suboptimize 141
Permutation problems 141
Locally optimal permutations 143
Calculation of locally optimal permutations 145
Choosing sets of exchanges 149
Multi-permutation problems 149
Heuristic techniques 152
The need for skilful guessing 152
The nature of allocation problems 153
Problem specification and mathematical treatment 161
Flexibility in problem formulation 161
The choice of the problem variables 162
Transferring factors between the objective and constraint functions 162
Introducing auxiliary variables 164
Transformations 166
Duality in linear problems 168
Interpretation of the dual problem 172
Proof of the duality theorem 174
Answers to exercises 178
Login|Complaints|Blog|Games|Digital Media|Souls|Obituary|Contact Us|FAQ
CAN'T FIND WHAT YOU'RE LOOKING FOR? CLICK HERE!!! X
You must be logged in to add to WishlistX
This item is in your Wish ListX
This item is in your CollectionOptimization In Industry, Volume 1
X
This Item is in Your InventoryOptimization In Industry, Volume 1
X
You must be logged in to review the productsX
X
X
Add Optimization In Industry, Volume 1, , Optimization In Industry, Volume 1 to the inventory that you are selling on WonderClubX
X
Add Optimization In Industry, Volume 1, , Optimization In Industry, Volume 1 to your collection on WonderClub |