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Chvatal V. — Linear programming
Chvatal V. — Linear programming



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Название: Linear programming

Автор: Chvatal V.

Аннотация:

Linear Programming was written primarily for upper-division and graduate courses in operations research/management science, mathematics, and computer science. It may serve not only as an introduction to the subject but also as a reference and guide to applications. When I taught in the Operations Research Department at Stanford University, I found that none of the available texts quite fit my presentation, so I wrote lecture notes and distributed them in class. The students' enthusiasm encouraged me to rework the notes into a manuscript.


Язык: en

Рубрика: Computer science/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1983

Количество страниц: 478

Добавлена в каталог: 10.06.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_{p}$-approximation      218
$L_{p}$-norm      218
Absolute values      189—191 222—223
Absorbance      214
Absorption spectrum      214
Accumulated rounding errors      74
Activity      173
Activity new variable      158—159
Activity, basic      104
Activity, entering      105
Activity, nonbasic      104
Acyclic network      296
Adding new constraint      159—160
Addition of matrices      84
Affine transformation      446
Aho, A. V.      282
Aircraft scheduling example      352
Algebra of matrices      84
Algorithms, efficiency of      51—52
Ali, A. I.      317
Allocation of scarce resources      171—173
Almon, C.      436
Alterable path      375
Alternative optimal solutions      22—23
Analytic coordinates      250
Anderson, D.      227
Antichain      340
Antosiewicz, H. A.      193
Appolonius of Perga      251
Approximate solutions      213 216—227
ARC      292
Arc, artificial      304 363
Arc, dummy      322
Arc, endpoint of      292
Arc, entering      298 300 360
Arc, forward      300 361
Arc, head of      292
Arc, leaving      300
Arc, return      368
Arc, reverse      300 361
Arc, saturaated      354
Arc, tail of      292
Arc, zero      310
Arithmetic, floating point      74
Arrays representing a tree      312—314
Artificial arc      304 363
Artificial variable      125—126 130—132
Aspvall, B.      451
Assignment problem      343
Associative law of matrix multiplication      81
Augmenting path      375
Augmenting path method      374—380
Auxiliary network      393
Auxiliary problem      39 126 304 363
Avis, D.      xiii 46 50
Away from a node      307
Back substitution      71—73
Backpath      315
Backward error analysis      75 409
Backward file      408
Backward transformation (BTRAN)      111 112 114 405—406
Balanced node      393
Balanced tree      282
Balinski, M. L.      373
Ball      270 see
Bartels — Golub method      409—410
Bartels, R. H.      406 409
Barth, G.      214
Basic activity      104
Basic feasible direction      242—243 278
Basic feasible partition      278
Basic feasible solution      19 100 120
Basic feasible solution, normal      134 244
Basic feasible solution, relationship with vertices of polyhedra      253 274
Basic solution      120
Basic solution, dual-feasible      157
Basic variable      20
Basis (=set of basic variables)      20 100 see
Basis heading      102
Basis matrix      100
Basis matrix, eta factorization of      xi 105—106 109—100
Basis matrix, relationship with spanning trees      296—297 319
Basis matrix, triangular factorization of      405—406
Basis matrix, working basis      417
Beale, E. M. L.      33
Beer — Bouguer's law      215
Beer, A.      214
Belz, M. H.      211
Berge, C.      229—230 234
Best fit      213 216—221
Bicycle problem      12
Big M method      128
Big O notation      380
Bin-packing problem      198 208
Bipartite graph      332 372 388
Birkhoff G.      330
Birkhoff-von Neumann Theorem      330
Bland's rule      see "Smalest-subscript rule"
Bland, R. G.      37 451
Blaschke, W.      267 270
Blattberg, R.      221
Block-angular problems      434—435 440—441
Block-triangular matrix      412
Blocking flow      383
Bloomfield, P.      227
Bluffing      235
Bogert, L. J.      185 187
Bonaparte, N.      227
Bonbon, T.      229—232 234
Bondy, J. A.      xiii
Borel, E.      228—234
Borgwardt, K. H.      46
Boscovich, R. J.      227
Bottleneck assignment problem      344
Botts, T.      269
Bouguer, P.      214
Bounded set      270 287
Bounded variable      see "Restricted variable"
Bounds on individual variables      119
Bowman, E. H.      323
Bradley, G. H.      312 317
Branch-and-bound method for the knapsack problem      206
Breadth-first search      280
Breakeven price      70
Briggs, G. M.      185 187
Brouwer, L. E. J.      228
Brunn, H.      262
BTRAN      111 112 114 405—406
Bump      91 412
Bunnenberg, E.      214
Calloway, D. H.      185 187
Capacitated transshipment problem      see "Upperbounded transshipment problems"
Capacity of a cut      370
Caratheodory, C.      265
Cartesian coordinates      see "Analytic coordinates"
Case study in forestry      171—176
Caterer problem      324—326
Cayley, A.      81
Center of ellipsoid      452
Center of simplex      446
Certificate of optimality      61—62
Chain      340 see
Changes in data      see "Sensivity analysis"
Charnes, A.      10 34 193
Cheap, Middling or Dear      239
Chebyshev approximations      see "$L_{\infty}$-approximations as a special case of $L_{p}$-approximation"
Chvatal, V.      12 46 50 239
Circling      see "Cycling"
Claerbout J. F.      221
Clark, D.      xiii
Column generation      198—200 428—429
Column player      230
Column singleton      413
Column vector      82
Column, entering      101
Column, eta      83
Column, leaving      102
Column, pivot      24
Combination, convex      330
Combination, linear      55 138
Comparison of the revised and the standard simplex methods      113—115
Complementary slackness      62—65 104—105 238
Complete pivoting      74
Component of a vector      82
Computer implementations of the network simplex method      311—317
Computer implementations of the simplex method      105—115 405—414
Connected network      296
Conservation law      369
Constrained variable      see "Restricted variable"
Constraints, linear      6
Constraints, linking      435
Convex closure      see "Convex hull"
Convex combination      330
Convex hull      263—265
Convex set      263
Convex set, separation theorem for      266
Cook, S. A.      336
coordinates      see "Analytic coordinates"
Core (in Dinic's algorithm)      381
core memory      113—115 406 408 412 413—414
Corner-point theorem      see "Fundamental Theorem of Linear Programming"
Cost vector      295
Cover      331 388
Cramer's rule      444
Cunningham's rule      307—310 335 365
Cunningham, W. H.      303 308
Cut      370
Cut, capacity of      370
Cutting-stock problem      195—212
CYCLE      296
Cycle, negative      362 402
Cycling      30—33 124 303
Dantzig — Wolfe decomposition algorithm      194 429—434
Dantzig — Wolfe decomposition algorithm, economic interpretation of      436—439 441
Dantzig — Wolfe decomposition principle      425—428 439—441
Dantzig, G. B.      7—9 34 37 45 46 57 97 105 119 193 194 228 291 336 339 391 416 435 436
Danzer, L.      267
de Buchet, J.      83
de Lucy, F.      xiii
Decentralized planning      436
Decision variable      14
Decomposition of a transshipment problem      305—306
Decomposition, Dantzig — Wolfe      425—442
Decomposition, LU      88
Degeneracy      29—30 124 259 302 361 362
Delayed column generation      198—200 428—429
Demand vector      295
Dense systems of linear equations      77
Depth of a node      313
Depth-first search      314
Descartes, R.      250—251
Destination      see "Sink"
Determinant      443—444
Devex      115
Dictionaries      xi 17—19
Dictionaries, dual-feasible      149—152
Dictionaries, feasible      19
Dictionaries, matrix description of      98—100
Diet problem      3—5 182—184 185—187
Dijkstra's algorithm      see "Shortest-paths algorithm"
Dijkstra, E.      391
Dilworth's Theorem      341
Dilworth, R. P.      340
DIMENSION      see "n-dimensional space"
Dimension analysis      66
Dinic's algorithm      384 389
Dinic, E. A.      380 384
Directed path      391
Direction      see "Basic feasible direction"
Displacement      398
Distance      269
Distinct representatives      336
Doig, A. G.      211
Domination between strategies      237
Dorfman, R.      68
Dot product      see "Scalar product"
Doubly stochastic matrix      329
Dry node      393
Drysdale, R. S.      xiii
Dual problem      56 139
Dual simplex method      152—157 175
Dual simplex method, revised format      153—157
Dual variables      see "Dual problem"
Dual variables, economic significance of      65—68 136
Dual-feasible basic solution      157
Dual-feasible dictionary      149—152
Duality theorem      8 58 141 261—262
Duality theorem, weak      140
Duffin, R. J.      242 286
Dummy nodes and arcs      322
Dyer, M. E.      282
Dynamic programming      206—207
Economic interpretation of the decomposition algorithm      436—439 441
Economic interpretation of the revised simplex method      102 105
Economic significance of dual variables      65—68 136
Economy models      68
Edge of a network or a graph      see "Arc"
Edge of a polyhedron      254—255
Edmonds, J.      51 331 336 380 391 400 444
Efficiency of algorithms      51—52
EFI      see "Elimination form of the inverse"
Egervary, J.      334 374 390
Eisemann, K.      196
Eisenhart, C.      227
Elias, P.      371
Elimination form of the inverse(EFI)      see "Triangular factorization"
Elimination of free variables      132—133
Elimination, Fourier — Motzkin      241—242
Elimination, Gauss — Jordan      xii 79
Elimination, Gaussian      xii 71—79 272 277 443—444
Ellipsoid      446
Ellipsoid method      xii 52
Endpoint of an arc      292
Entering activity      105
Entering arc      298 300 360
Entering column      101
Entering variable      21 28 121 124
Entry of a matrix      81
Enumeration trees      201—202
Equations      see "Linear equation"
Equilibrated systems of linear equations      76
Equivalence of game theory and linear programming      232 239
Equivalence of spanning trees and bases in a transshipment problem      296—297 319
Error analysis      75 409
Error tolerances      see "Zero tolerances"
Eta column      83
Eta factorization of the basis      xi 105—106 109—110
Eta file      110—112
Eta matrix      83
Euclidean norm      see "$L_{2}$-norm as a special case of $L_{p}$-norm"
Euclidean space      see "n-dimensional space"
Eves, H.      74
Extreme points of a polyhedron      see "Vertices of a polyhedron"
Facets of a polyhedron      252
Factorization of the basis, eta      xi 105—106 109—110
Factorization of the basis, triangular      405—406
Fair game      233
Fama, E. P.      221
Farkas's lemma      248
Farkas, J.      248
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