Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Bazaraa M.S., Sherali H.D., Shetty C.M. — Nonlinear Programming: Theory and Algorithms
Bazaraa M.S., Sherali H.D., Shetty C.M. — Nonlinear Programming: Theory and Algorithms

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Nonlinear Programming: Theory and Algorithms

Авторы: Bazaraa M.S., Sherali H.D., Shetty C.M.

Аннотация:

Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.

Concentration on the three major parts of nonlinear programming is provided:

- Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming
- Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions
- Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems

Important features of the Third Edition include:

- New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more
- Updated discussion and new applications in each chapter
- Detailed numerical examples and graphical illustrations
- Essential coverage of modeling and formulating nonlinear programs
- Simple numerical problems
- Advanced theoretical exercises

The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programmi


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Third edition

Год издания: 2006

Количество страниц: 853

Добавлена в каталог: 12.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\ell_{1}$ norm      334
$\ell_{1}$ penalty function      487
$\ell_{p}$ norm metric      25
$\eta$-invex function      234
$\eta$-pseudoinvex function      234
$\eta$-quasi-invex function      234
$\lambda$-form approximation      685 741
(m + 1)-step process      433
Abadie's Constraint Qualification      248
Absolute value or $\ell_{1}$ penalty function      487
Acceleration step      367 368
Active constraints      177
Active nodes      678
Active set approach      651
Active set method      732
Active set strategy      738 747
Addition of matrices      753
Adjacent almost complementary basic feasible solution      659
Affine      98 148 752
Affine combination      40 752
Affine hull      42
Affine hulls      752
Affine independence      751
Affine manifold      150
Affine scaling variant      634
Affinely independent      43 751
Aitken double sweep method      365
ALAG penalty function      500
Algorithm      317
Algorithmic map      317
Almost complementary basic feasible solution      659
Alternative optimal solutions      2 124
AMPL      36
Approximating problem      687
Approximating the separable problem      684
Approximation programming      650
Armijo's inexact line search      392
Armijo's Rule      362
Arrow — Hurwicz — Uzawa constraint qualification      254
Artificial variables      83
Ascent direction      283
Aspiration level      21
Augmented Lagrangian      534
Augmented Lagrangian penalty function (ALAG)      471 490 491 495
Augmented Lagrangian penalty methods      485
Auxiliary function      471 502
Average convergence rates      341
Average direction strategy      441 467
Average rates of convergence      332
Ball      760
Baron      36
Barrier function methods      501 503 508 512 536
Barrier problem      501
Basic feasible solution      68
Basic vector      603
Basis      77 752
BFGS update      417
Big-M method      83
Bilinear program      226 645
Bilinear programming problem      657
Bimatrix game      726
Binding constraints      177
Bisection search method      356 357
Block halving scheme      440
Bordered Hessian      770
Bordered Hessian determinants      137
Bound-constraint-factor product inequalities      682
Bound-factor product      737
Bound-factor product inequality      682
Boundary      45 761
Boundary point      761
Bounded      45 761
Bounded sets      761
Bounding and scaling      29
Box-step method      401
Branch-and-bound algorithm      678 738
Branching variable      679 680
Broyden family updates      416
Broyden — Fletcher — Goldfarb — Shanno update      416
Bundle algorithms      467
Bundle methods      442
Canonical form      91
Caratheodory theorem      43
Cauchy point      402
Cauchy sequence      761
Cauchy's method      384
Central path      511
Chance constrained problems      35
Chance constraint      21 22
Characterization of optimality      86
Chemical process optimization      36
Children hyperrectangles      679
Choice of step sizes      439
Cholesky factor      759
Cholesky factorization      154 419 758
Classical optimization techniques      165
Closed      45 761
Closed half-spaces      52
Closed interval      760
Closed maps      321
Closed maps and convergence      319
Closed sets      761
Closedness of the line search algorithmic map      363
Closest-point theorem      50
Closure      45 761
Closure points      761
Cofactor      754
Column vector      751
Compact      762
Compact set      45
Comparison among algorithms      329
Complementarity constraints      657
Complementary basic      660
Complementary basic feasible solution      657
Complementary cone      657
Complementary feasible solution      657
Complementary slack solutions      86
Complementary slackness condition      86 183 191 772 773
Complementary update      419
Complementary variables      656
complexity      122
Complexity analysis      516
Component      751
Composite dual      313
Composite map      324 326
Composition of mappings      324
Computational comparison of reduced gradient-type methods      653
Computational difficulties associated with barrier functions      507
Computational difficulties associated with penalty functions      481
Computational effort      330
Concave      98 767
Condition number      389
Cone of attainable directions      242
Cone of feasible directions      174 242
Cone of improving directions      174
Cone of interior directions      242
Cone of tangents      93 237 238 250
Cone spanned      752
Cone spanned by a finite number of vectors      765
conjugate      403
Conjugate directions      402 407
Conjugate dual problem      313
Conjugate functions      312
Conjugate gradient methods      402 422 420
Conjugate subgradient algorithm      534
Conjugate weak duality theorem      313
CONOPT      36
Constraint qualifications      189 773 241
Constraint-factor product inequalities      682
Continuity of convex functions      100
Continuous at $\bar{x}$      762
Continuous functions      762
Continuous optimal control      6
contour      3
Control problem      311
Control vector      4
Converge      319
Converge to the limit point      761
Convergence      331
Convergence analysis for the RLT algorithm      680
Convergence analysis of the gradient projection method      599
Convergence analysis of the method of Zoutendijk      557
Convergence analysis of the quadratic programming complementary pivoting algorithm      671
Convergence analysis of the steepest descent algorithm      392
Convergence of algorithms      318 326
Convergence of conjugate direction methods      432
Convergence of Newton's method      359
Convergence of the bisection search method      357
Convergence of the complementary pivoting algorithm      663
Convergence of the cutting plane algorithm      338
Convergence of the cyclic coordinate method      367
Convergence of the method of Rosenbrock      381
Convergence of the method of Topkis and Veinott      564
Convergence of the reduced gradient method      609
Convergence of the simplex method      80
Convergence of the steepest descent method      387
Convergence rate analysis      516 579
Convergence rate analysis for the steepest descent algorithm      389
Convergence rate characteristics for conjugate gradient methods      433
Convergence rate characteristics for Quasi — Newton methods      434
Convergence ratio      331
Convex      40 98 765 767
Convex combination      40 752 765
Convex cone      41 62 63
Convex envelope      151 736
Convex extension      159
Convex functions      767 769
Convex hull      40 42 752
Convex programming problems      125
Convex quadratic programming      667
Convex sets      765
Convex-simplex method      613 705
Convexity at a point      145
Coordinate vector      751
Copositive      665
Copositive-plus      665
Corrector step      519
Cottle's constraint qualification      244 248
Covariance matrix      20
Created response surface technique      533
Criterion function      2
Cumulative distribution function      149
Curvilinear directions      180
Cutting plane      441 442
Cutting plane algorithm      338
Cutting plane method      289 290 337
Cyclic coordinate method      366 365
Cycling      80
Data fitting      36
Davidon — Fletcher — Powell (DFP) method      408 414
Definite matrices      756
Deflected negative gradient      335
Deflecting the gradient      389
Degenerate      418
Degree of difficulty      717 720
Dense equation systems      757
Derivative-free line search methods      354
Descent direction      167 174
Descent function      321 323
Design variables      17
Determinant of a matrix      754
Diadic product      736
Diagonal matrix      755
Diagonalization process      755
Dichotomous search      347
Dichotomous search method      348
Differentiability      277
Differentiable at $\bar{x}$      763
Differentiable functions      763
Differentiable quasiconvex functions      137
Differentiate      109
Dimension of the set      94
Direct optimization techniques      99
Direction      66 767
Direction of descent      155
Direction of steepest ascent      284
Direction-finding routine for a convergent variant of the gradient projection method      601
Direction-finding subproblem      571
Directional derivative      102
Discrepancy index      679
Discrete control problem      5
Discrete optimal control      4
Distance function      149
Distinct directions      67
Dog-leg trajectory      402
Dorn's dual quadratic program      300
Dual      84
Dual feasibility condition      191
Dual feasibility conditions      183
Dual function: properties      278
Dual geometric program      716
Dual problem      258
Dual update      419
Dual variables      258
Duality gap      264
Duality in linear programming      84
Duality theorems      263
Dualization      258
Dualized      286
Eccentricity ratio      12
Economic interpretations      275
Effect of near-binding constraints      556
Effective domain      159
Efficient      31
Efficient portfolio      31
Eigenvalue      755
Eigenvector      755
Either-or constraints      159
Elastic constraints      28
Electrical networks      13
Element      751
Empty set      759
Ending node      14
Epigraph      104
Equality constraint      2
Equilibrium problems      36
Error estimations      694
Error function      391
Euclidean      25 334
Euclidean norm      752
Exact absolute value penalty methods      485
Exact penalty function      485 487 491
Expanding subspace property      405
Explicitly quasiconvex      139
Exploratory search      368
Exterior penalty function method      475 479
Extreme direction      65 67 70
Extreme directions: existence      74
Extreme point: initial      82
Extreme points      65 67
Extreme points: existence      69
Factorable programming problems      748
Factorizations      331
Farkas's theorem      767
Fathom      678
Feasible direction      174 538 561
Feasible direction algorithms      537
Feasible direction method      129
Feasible direction method of Topkis and Veinott      561
Feasible region      2 75
1 2 3 4
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте