|
|
Авторизация |
|
|
Поиск по указателям |
|
|
|
|
|
|
|
|
|
|
Sinha S.M. — Mathematical Programming: Theory and Methods |
|
|
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
|
|
|
Реклама |
|
|
|