Linear and Nonlinear Programming: Second EditionThe original edition of this book was celebrated for its coverage of the central concepts of practical optimization techniques. This updated edition expands and illuminates the connection between the purely analytical character of an optimization problem, expressed by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. Incorporating modern theoretical insights, this classic text is even more useful. |
Contents
I | 1 |
III | 2 |
IV | 5 |
V | 6 |
VI | 11 |
VIII | 14 |
IX | 17 |
X | 18 |
LXXIX | 263 |
LXXX | 265 |
LXXXI | 268 |
LXXXII | 271 |
LXXXIII | 275 |
LXXXIV | 279 |
LXXXV | 282 |
LXXXVI | 287 |
XI | 21 |
XII | 26 |
XIII | 30 |
XV | 36 |
XVI | 40 |
XVII | 44 |
XVIII | 48 |
XIX | 53 |
XX | 58 |
XXI | 59 |
XXII | 65 |
XXIII | 68 |
XXIV | 75 |
XXV | 76 |
XXVI | 85 |
XXVIII | 88 |
XXIX | 90 |
XXX | 95 |
XXXI | 97 |
XXXII | 99 |
XXXIII | 104 |
XXXIV | 110 |
XXXV | 117 |
XXXVII | 121 |
XXXVIII | 123 |
XXXIX | 126 |
XL | 133 |
XLI | 134 |
XLII | 137 |
XLIII | 141 |
XLIV | 149 |
XLV | 157 |
XLVI | 158 |
XLVII | 167 |
XLVIII | 168 |
XLIX | 170 |
L | 174 |
LI | 176 |
LII | 180 |
LIII | 182 |
LIV | 189 |
LV | 193 |
LVI | 194 |
LVII | 196 |
LVIII | 197 |
LIX | 200 |
LX | 207 |
LXI | 209 |
LXII | 211 |
LXIII | 214 |
LXIV | 220 |
LXV | 225 |
LXVI | 227 |
LXVII | 230 |
LXVIII | 231 |
LXIX | 232 |
LXX | 238 |
LXXI | 241 |
LXXII | 243 |
LXXIII | 246 |
LXXIV | 248 |
LXXV | 252 |
LXXVI | 254 |
LXXVII | 257 |
LXXVIII | 260 |
LXXXVII | 288 |
LXXXVIII | 295 |
LXXXIX | 297 |
XC | 300 |
XCI | 301 |
XCII | 306 |
XCIII | 308 |
XCIV | 312 |
XCV | 314 |
XCVI | 318 |
XCVIII | 322 |
XCIX | 323 |
C | 326 |
CI | 330 |
CII | 337 |
CIII | 345 |
CIV | 350 |
CV | 357 |
CVI | 359 |
CVII | 360 |
CVIII | 365 |
CX | 366 |
CXI | 369 |
CXII | 371 |
CXIII | 378 |
CXIV | 380 |
CXV | 382 |
CXVI | 384 |
CXVII | 387 |
CXVIII | 391 |
CXIX | 392 |
CXX | 396 |
CXXII | 397 |
CXXIII | 402 |
CXXIV | 403 |
CXXV | 406 |
CXXVI | 411 |
CXXVII | 416 |
CXXVIII | 418 |
CXXIX | 420 |
CXXX | 421 |
CXXXI | 423 |
CXXXIV | 427 |
CXXXV | 433 |
CXXXVI | 435 |
CXXXVII | 439 |
CXXXVIII | 444 |
CXXXIX | 446 |
CXL | 449 |
CXLI | 450 |
CXLII | 455 |
CXLV | 456 |
CXLVI | 457 |
CXLVII | 458 |
CXLVIII | 459 |
CXLIX | 460 |
CL | 464 |
CLI | 465 |
CLII | 468 |
CLIII | 470 |
CLIV | 472 |
476 | |
487 | |
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Common terms and phrases
active constraints algorithm applied approximation assume basic feasible solution basic solution basic variables basis column components computational conjugate gradient method constrained problem convex set corresponding defined determined dual problem eigenvalues equality constraints equations Example extreme points feasible direction formula global convergence gradient projection method hence Hessian Hessian matrix inequality constraints iterative Lagrange multipliers Lagrangian line search linear programming problem matrix maximal flow minimize subject Newton's method node nonlinear programming nonnegative nonzero objective function obtain optimal solution original problem orthogonal penalty function pivot positive definite primal problem minimize f(x Proof quadratic program quasi-Newton methods rate of convergence reduced gradient method relative cost coefficients result satisfying Section sequence Show simplex method solved steepest descent step subject to h(x subspace Suppose tableau Theorem transportation problem triangular unconstrained update vector Vf(x x₁ xk+1 zero