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Sinha S.M. — Mathematical Programming: Theory and Methods
Sinha S.M. — Mathematical Programming: Theory and Methods

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Название: Mathematical Programming: Theory and Methods

Автор: Sinha S.M.

Аннотация:

Mathematical Programming, a branch of Operations Research, is perhaps the most efficient technique in making optimal decisions. It has a very wide application in the analysis of management problems, in business and industry, in economic studies, in military problems and in many other fields of our present day activities. In this keen competetive world, the problems are getting more and more complicated ahnd efforts are being made to deal with these challenging problems. This book presents from the origin to the recent developments in mathematical programming.
The book has wide coverage and is self-contained. It is suitable both as a text and as a reference.

* A wide ranging all encompasing overview of mathematical programming from its origins to recent developments
* A result of over thirty years of teaching experience in this feild
* A self-contained guide suitable both as a text and as a reference


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 572

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Activity vectors      120
Affine set      27
angle      37
Artificial variable      145
Augmented matrix      63
Augmented matrix, consistent      63
Augmented matrix, equivalent      63
Augmented matrix, homogeneous      63
Augmented problem      206
Auxiliary primal      211
Basic solution      67 120 121
Basic solution, basic feasible solution      121
Basic solution, nondegenerate basic feasible      121
Basic variables      67 121
Basis      31 121
Bessel inequality      35
Big M-method      150
Bounded functions      20
Caratheodory's theorem      80
Cayley Hamilton theorem      60
Chain rule      24
Characteristic equation      60
Characteristic polynomial      60
Characteristic value      59 60
Characteristic vector      59
Charnes and Cooper      3
Closed and open intervals      14
Coefficient matrix      63
Cofactor      44
Cofactor, adjoint matrix      45
Cofactor, nonsingular      46
Cofactor, singular      46
Complementary basic feasible solution      357
Complementary slackness      185
Complementary slackness, strong      186
Concave functions      94
Cone      91
Cone, convex cone      91
Cone, polar cone      91
Cone, polydral convex cone      93
Constraint qualification      329
Constraint qualification, Kuhn — Tucker constraint qualification      330
Constraints      120
Continuous functions      20
Continuous functions, lower and upper semicontinuous functions      20
Convex      76 91
Convex function      94
Convex function, strictly convexs      94
Convex simplex method      409
Convex, convex combination      77
Convex, convex cones      91
Convex, convex sets      76
Copositive matrix      359
Copositive-plus matrix      359
Cutting plane method      374
Dantzig      2 3
Dantzig's method for convex programs      414
Decomposition      292
Decomposition, block-angular matrix      292
Decomposition, bounded subprogram      292
Decomposition, decomposition algorithm      294
Decomposition, unbounded subprogram      296
Degeneracy      67 158
Degeneracy, lexicographic method      159
Degeneracy, perturbation method      159
Descent direction      324
Determinants      43
Differentiable functions      22
Differentiable functions, composite function      23
Differentiable functions, vector function      23
DIMENSION      33
Direction      77
Direction, convex combination      78
Direction, convex hull      79
Direction, extreme direction      77
Distance      36
Dual feasible      199
Dual simplex method      199
Duality      177
Duality in goal programms      467
Duality, and Lagrange multipliers      189
Duality, duality in fractional programming      488
Duality, duality in nonlinear programming      423
Duality, duality in nonlinear programs with linear constraints      426
Duality, duality in quadratic programming      427
Duality, duality theorems      177
Duality, in linear programming      177
Dynamic programming      502
Echelon matrix      54
Eigenvalues      60
Eigenvectors      60
Elementary matrix      53
Epigraph      98
Equivalent matrix      55
Euclidean space      34
Explicitly quasiconvex      109
Extreme points      77
Faces      90
Farkas' Lemma      194
Farkas' lemma, economic interpretation      195
Farkas' theorem      92 69
Feasible directions      327 380
Feasible set      120
Feasible solution      120
Fields      26
Fractional programming      479
Fractional programming, Dinkelbach's algorithm      486
Fractional programming, generalized fractional programs      490
Fractional programming, homogenous fractional programs      489
Fractional programming, linear fractional programming      481
Fractional programming, method of Charnes and Cooper      481
Fractional programming, multiobjective fractional programs      495
Fractional programming, non differentiable fractional programs      489
Fractional programming, nonlinear fractional programming      484
Fractional programming, quadratic fractional programs      488
Fritz John      333
Functions      19
Functions, numerical function      19
Functions, vector-valued function      19
Gale, Kuhn and Tucker      3
Global minimum      324
Global minimum point      99
Global minimum point, continuity of convex functions      100
Global minimum point, differentiable convex functions      101
Global minimum point, twice differentiable convex functions      103
Goal efficiency      466
Goal programming      462
Gordan's Theorem      72
Gradient projection method      394
Grid points      367
Grid refinement      372
Half line      76
Half-spaces      76
Hessian matrix      24
Hyperplane      76
Hyperplane, normal      76
Hyperplane, parallel      76
Hypograph      113
Implicit function theorem      24
Incommensurability in good programmings      466
Inconsistency      155
Indefinite quadratic programming      496
Inequalities      68
Infimum of functions      21
Inner product      34
Inner product space      34
Interactive G.P.      467
Jacobian      23
Karmarkar's algorithm      311
Khachiyan's ellipsoid method      304
Khachiyan's ellipsoid method, complexity      316
Khachiyan's ellipsoid method, convergence      311
Khachiyan's ellipsoid method, conversion of a general linear program      316
Lagrange multipliers      3
Latent roots      60
Length      34
Leontief      2
Level set      98
Line      76
Line segment      76
linear combination      27
Linear dependence      28
Linear program      120
Linear programming      2 117
Linear space      28
Linear transformation      50
Linear transformation, elementary transformations      52
Linear transformation, nonsingular      51
Linear transformation, orthogonal      51
Linear transformation, product of linear transformations      51
Linear transformation, the rank of a linear transformation      51
Linear variety      27
Local minimum      99 324
Lower bound      236
Mappings      19
Matrices      38
Matrices, addition      39
Matrices, diagonal matrix      39
Matrices, equality      39
Matrices, idempotent matrix      41
Matrices, identity matrix      39
Matrices, matrix      39
Matrices, multiplication by a scalar      40
Matrices, nonsingular      43
Matrices, orthogonal matrix      41
Matrices, partitioning of matrices      41
Matrices, product of two matrices      40
Matrices, rank of a matrix      42-43
Matrices, regular      43
Matrices, singular      43
Matrices, skew symmetric matrix      39
Matrices, square matrix      38
Matrices, submatrix      41
Matrices, symmetric      39
Matrices, trangular matrix      39
Matrices, transpose of a matrix      39
Matrices, transpose of the product      41
Matrices, unit matrix      39
Matrix      121
Mean value theorem      24
Method of feasible directions      379
Method of penalties      150
Metric space      36
Minima and maxima of functions      21
Minor      44
Modified primal      218
Motzkin's theorem      73
Multiphase goal programming      466
Multiple objective linear programming      467
Multiple objective linear programming, Echer-Kouda method      475
Multiple objective linear programming, efficient faces      470
Multiple objective linear programming, efficient point      469
Multiple objective linear programming, efficient solution methods      468
Multiple objective linear programming, Evans-Stener method      472
Multiple objective linear programming, Iserman's method      477-478
Multiple objective linear programming, properly efficient      469
Multiple objective linear programming, ranking or prioritizing methods      468
Neighbourhoods      16
Neighbourhoods, boundary points      17
Neighbourhoods, bounded sets      18
Neighbourhoods, closed sets      17
Neighbourhoods, compact sets      18
Neighbourhoods, open sets      17
Neighbourhoods, relatively open (closed) sets      17
Nonbasic variables      67 121
Nonlinear program      2
Nonlinear programming      9
Nonnegative restrictions      120
Norm      34
Normal vector      35
Normalization constraint      384
Normalization requirement      383
Normed vector space      35
Objective function      120
Optimal conditions      333
Optimal conditions, linear independence constraint qualification      334
Optimal conditions, Slater's constraint qualification      334
Optimal conditions, Zangwill constraint qualification      333
Optimal solution      120
Orthogonal      34
Orthonormal set      35
Parametric programming      222
Partial derivatives      22
Polynomial time algorithms      303
Pre-emptive goal programming      464
Primal-dual algorithm      199
Projection matrix      395
Pseudoconvex function      110
Quadratic form      56
Quadratic form, indefinite      57
Quadratic form, matrix of the quadratic form      56
Quadratic form, negative definite      57
Quadratic form, negative semidefinite      57
Quadratic form, positive definite      57
Quadratic form, positive semidefinite      57
Quadratic form, rank of the quadratic form      56
Quasiconvex function quasiconcave      104
Quasiconvex function quasiconcave, strictly quasiconcave      107
Quasiconvex function quasiconcave, strictly quasiconvex functions      107
Ray termination      359
Reduced gradient method      403
Redundancy      155
Requirement vector      120
Restricted primal      210
Revised simplex method      166
Saddle point      189
Saddle point problem      335
Saddle value problem      189
Schwarz inequality      36
Sensitivity analysis      222
Sensitivity analysis in G.P.      466
Separable programming      366
Separating hyperplane      82
Separation of two sets      85
Separation of two sets, convex hull      88
Separation of two sets, convex polyhedron      88
Separation of two sets, convex polytopes      87
Sequences and subsequences      18
Sequences and subsequences, cauchy sequence      19
Sequences and subsequences, limit of a sequence      18
Sequences and subsequences, limit point      18
Sets      13
Sets, greatest lower bound and least upper bound      15
Sets, lower and upper bounds      15
Sets, operations on sets      13
simplex      90 132
Simplex algorithm      136
Simplex method      132
Simplex tableau      137
Simplex, pivot element      137
Simplex, replacement operation      138
Simplex, replacement rule      140
Slack variable      120
Stationary points      325
Stiemke's theorem      73
Stochastic linear programming      431
Stochastic linear programming, distribution problem      432
Stochastic linear programming, expected volume model      431
Stochastic linear programming, here and now models      432
Stochastic linear programming, minimum variance model      431
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