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