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Pedregal P. — Introduction to Optimization

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Название: Introduction to Optimization

Автор: Pedregal P.

Аннотация:

This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed.

Язык:

Рубрика: Математика/Оптимизация и управление/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 244

Добавлена в каталог: 23.04.2005

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Предметный указатель

Accelerator      200 208 215 227
Action integral      153
Active and reactive powers      3
Admisible vectors      29
Aerodynamical effects      233
Affine function      96
Augmented functional      197
Augmented integrand      160
Augmented Lagrangian      130
Augmented Lagrangian method      128
Barrier      125
Basic functions      186
Basic solutions      30
Basic step of the simplex method      33
Bellman’s equation      184 205
Bending and buckling      175
Boat manufacturer      5 13
boundary conditions      139
Bounded set      68
Bounded surface      72
Bounds on controls      204
Brachistochrone      145 194
Branch and bound method      60
Branching      60
Broyden — Goldfarb — Shanno algorithm      120
Catenary      149 164
Change in the dynamics      209
Circuit      234
Cobb — Douglas utility function      17 108
commodities      17
Competing functions      138
Computational cost      113
Conjugate directions      120
Conservative field      152
Constraints      7 8
consumption      20 222
Convex function      88
Convex set      88
Convexification      94
Convexity      140 201
Cooling law      235
Costate      197 206
Critical points      107
Current      234
Curvatures      175
Cushioning force      21
Cyclic infinite process      66
Cycloid      147
Cylindrical container      173
Cylindrical coordinates      143
Davidon — Fletcher — Powell algorithm      119
Decay rate of sales      233
Degenerate cases      47
Degenerate example for the simplex method      39
density      18 109
Depreciation      20 222
Descent direction      117
Design of a channel      4 13 164 189
Diet problem      2 10
Differential element of arc length      146
Dirichlet’s integral      151
Discretization      185 227
Divergence theorem      157
Dual formulation      46
Dual function      102 127
Dual method      127
Dual prices      48
Dual problem      43 57
Dual problem in standard form      44
Duality gap      104
Duality link      46
Duality theorem      47
Economic growth      20
Efficiency of the algorithm      113
Eigenvalues      90 93
Ejection velocity      19
Elasticity of marginal utility      223
Electrical network      82
Elementary operations that respect convexity      93
Elongation      16 18 109
Endpoint restrictions      198
Entering variable      32
Equilibrium      2 5 16 18 152
Euler — Lagrange equation      141
Existence of optimal solutions      68
Extremal points      30
extreme values      70
Feasible function      138
Feasible region      24
Feasible set      25
Feasible vectors      25
Fibonacci sequence      116
Final state      224
First order problems      173
Flat parts of the graph      93
Fletcher — Reeves algorithm      124
Flux of fuel      233
force      16
Fourth order differential equation      175
Friction coeficcient      4
Fuel expenditure      200 227
Full — rank matrix      30
Fundamental property of dynamic programming      179
Fundamental theorem of calculus      183
Geodesics      143 190
Golden section      115
Gradient of the objective function      117
Hamiltonian      198
Hamilton’s principle      152
Hanging cable      162 194
Harmonic function      152
harmonic oscillator      5 213 232 236
Harmonic oscillator with friction      13
Hessian matrix      90 93 118
Heuristic algorithms      131
Higher derivatives      139
Hooke’s law      16 19 109
Hydraulic cushion unit      21
Hydraulic diameter      4
Hyperbolic trigonometric functions      149
Identity matrix      26
Inactive constraint      79
Infeasible solution      35
Infinite barrier      126
Infinite dimensional optimization problems      185
Infinitesimal element of arc length      163
Initial and/or final conditions      196
Initial iterate      131
Initialization of the simplex method      36 49
Integer values      59
Integral constraints      139 160
Integral cost functional      140
Integration by parts      155 157
Interior-point methods      29
Investor      15 65
Irrotational wind field      17
Iteration      112
Joint convexity      155
Labor growth      222
Lagrangian      103 128 137 153
Least energy      153
Least time      208
Leaving variable      32 35
Level curves      25
Line search      114
Linear dependence      75
Local and global minima      69 89 95
Logarithmic barrier      126

Marketing      233
Mathematical formulation      7
Mathematical programming      14
Maximum deflection      100
Maximum entropy principle      192
Maximum height      233
Maximum volume      83
Mean value theorem      91
Measure of the error      113
Min-max operation      106
Minimal surfaces      148 150 153 188
Minimum action      152
Minimum distance      98
Minimum time      210 222
Minimum weight      100
Moving solid      3 12 193
Multiple solution for the simplex method      42
Natural boundary condition      158 175
Necessary conditions of optimality      69
networks      45
Newton’s law      152
Newton’s method      118
No solution for the simplex method      40
Nodal values      186
Nonbinding constraint      79
Noncontinuous problems      169
Nonconvex example      142
Nonexistence      224
Nonsmooth optimization      75
Nonsmooth problems      169
Normal pressure      4
Numerical integrator      232
Numerical optimization      132
Nutritive contents      2
Objective or cost function      7
Obstacle problem      193
Obstacles      222
One-dimensional minimization      114
One-sided minimum      220
Optimal global solutions      131
Optimal strategy      210
Optimality conditions      198
Optimality criterion      7
Order of the problem      173
Outer normal      4
Parametrized curves      73
Penalization      125
Penalization parameter      126
Perimeter      13
Piecewise affine function      185
Pointwise constraints      139
Polak — Ribiere algorithm      124
Polygon      25
Polyhedron      25 31
Positioning problem      6 13
Positive definite matrix      118
potential energy      163 173
Potential fall      235
Power circuit state      3 11
Preassigned precision      115
PREDATOR      236
prices      17
Primal formulation      46
Primal problem      43 57
Production function      222
Publicity      233
Quadratic error      17 109
Quadratic functional      121
Quadratic penalization      126 129
Quadrature formula      17
Quadrature rule      187
Quasi — Newton algorithms      119
Radial symmetry      173
Ratio of invesment      222
Refracting medium      20
Resources      17
Rugosity      4
Sales level      233
Saturation of sales      233
Scaffolding system      2 10 15 65
Search direction      113
Secants      90
Second Order ODE      141
Second order problems      173
Sensitivity parameters      48
Servomechanism      5
Shadow prices      48
Singular points      75
Slack variables      26 130
Slowest descent      19
Soap film      150
software packages      14 112
Spaceships      235
springs      16 65
Standard form of an LPP      25
Standard form of an NLPP      68
State equation      195
Stationary state      152
Steepest descent      117
Step size      114
Step-size parameter      113
Stopping criterion of the simplex method      34
strain      19
Stress      19
Strict convexity      92 96 141
Subdeterminants      93
Successive approximations      112
Sufficiency of optimality conditions      220
Surface tension      150
Switching curves      211
Sylvester’s criterion      93
Symmetry      71
Tableaux      43 49 52
Tangent hyperplane      90
Taylor’s expansion      118
Thin elastic rods      175
Threshold precision      115
Threshold value      116
Thrust of the engine      233
Time discount factor      20
Time discount parameter      223
Time horizon      196
Total energy      20
Transit time      146
Transportation problem      2 9 65
Transversality      158 175
Transversality conditions      198 207
Transversality statement      198
Trapezoidal rule      188
Truncated-conic bar      109
Truss structure      100
Two-component control      218
Unique solution, example      37
Uniqueness      96 156
Utility function      17 223
Value function      181 207
Vandermonde determinant      73
Variational problems      14
Vector of reduced costs      33
Vertex      25
Voltage difference      234
Wave equation      152
Weak duality      47 104
Weierstrass’s example      144
Welfare integral      20 223
Work      16
Young modulus      18 109
Zero order problems      173

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