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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



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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
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Предметный указатель
PLU factorization      756
Polar cone      63
Polar set      88
Polarity      62
Polyak — Kelly cutting plane method      442 467
Polyhedral cone      765
Polyhedral set      40 65
Polynomial function      737
Polynomial in the size of the problem      517
Polynomial programming problem      655 668 737
Polynomial-time complexity      517
Polynomial-time interior point algorithms      509
Polytope      43
Portfolio selection problem      31
Positive definite      756
Positive definite secant update      417
Positive semidefinite      113 115 756
Positive subdefinite      157
Posynomial      712
Posynomial programming problems      712
Powell — Symmetric Broyden (PSB) update      453
Practical line search methods      360
PRECISION      329
Preconditioning matrix      428
Predictor step      519
Predictor-corrector algorithms      519
Predictor-corrector approach      519
Predictor-corrector variants      535
Preparational effort      330
Pricing phase      622
Primal feasibility condition      183 191
Primal feasible solutions      296
Primal methods      537
Primal problem      84 257 258 775
Primal solution      293
Primal-dual path-following      537
Primal-dual path-following algorithm      513
Principal pivoting method      659 725 746
Principal submatrix      771
Problems having inequality and equality constraints      197 245
Problems having inequality constraints      174
Problems having nonlinear inequality constraints      547
Production-inventory      5
Programming with recourse      35
Projected      576
Projected Hessian matrix      624
Projected Lagrangian      650
Projected Lagrangian approach      576
Projecting      435
Projecting the gradient in the presence of nonlinear constraints      599
Projection matrix      589
Proper convex function      159
Proper supporting hyperplane      57
Properly separate      53
Pseudoconcave      142
Pseudoconvex functions      142 768 770
Pseudoconvexity at $\bar{x}$      146
Pseudolinear      157
Pure Broyden update      417
Purified      517
q-order convergence rates      341
QR decomposition      759
QR factorization      757
QRP factorization      757
Quadratic      332
Quadratic approximation      153
Quadratic assignment program      223
Quadratic case      412 423
Quadratic form      755
Quadratic functions      405
Quadratic penalty function      480
Quadratic programming      15 21 24 298 299 311 576
Quadratic rate of convergence      331
Quadratic-fit algorithm      446
Quadratic-fit line search      361
Quasi-Newton      402
Quasi-Newton approximations      581
Quasi-Newton condition      416
Quasi-Newton procedures      407
Quasiconcave      135
Quasiconvex      768
Quasiconvex functions      134 771
Quasiconvexity at $\bar{x}$      145
Quasimonotone      135
r-(root)-order      332
r-order convergence rates      341
Rank of a matrix      754
Rank-one correction      467
Rank-one correction algorithm      455
Rank-two correction procedure      408
Rank-two correction procedures      464
Rank-two DFP update      416
Ray termination      660 662
Real Euclidean space      4
Recession direction      66
Rectilinear      25
Recursive linear programming      568
Recursive programming approaches      576
Reduced cost coefficients      81
Reduced gradient      605
Reduced gradient algorithm      602 605
Reduced gradient methods      653
Reformulation linearization/convexification technique (RLT)      667 668 676 712 736 748
Reformulation step/phase      668 676
Regular      205
Relative interior      94 760
Relative minima      124
Reliability      329 330
Remainder term      109
Representability      26
Representation of polyhedral sets      72
Representation theorem      72
response surface methodology      36
Restarting conjugate gradient methods      430
Restricted basis entry rule      687
Restricted Lagrangian function      212
Restricted step methods      400
Risk aversion constant      23
Risk aversion model      22
River basin      17
RLT      667 668 675 712 736 746
RLT Algorithm to Solve Problem NQP      679
RLT constraints      735
RLT constraints: cubic      683
RLT variables: cubic      734
Robustness      330
Rocket launching      7
Rosenbrock's method      376
Rosenbrock's method using line searches      382
Rosenbrock's method with discrete steps      382
Rounded      517
Row vector      751
Rudimentary SQP algorithm      579
Saddle point      172 269
Saddle point criteria      269 271
Saddle point optimality      269
Saddle point optimality conditions      213 263
Saddle point optimality interpretation      273
Safeguard technique      360
Satisficing criteria      21
Satisficing level      21
Scalar multiplication of a matrix      753
Scale invariant      330
Scale-invariant algorithms      29
Scaling of Quasi — Newton algorithms      420
Schwartz inequality      47 752
Secant equation      416
Second-order (Taylor Series)      112 113
Second-order conditions      167
Second-order cone of attainable directions constraint qualification      252
Second-order constraint qualification      249
Second-order functional approximations      622
Second-order necessary and sufficient conditions for constrained problems      211
Second-order necessary condition      775
Second-order rate of convergence      331
Second-order sufficient conditions      775
Second-order variants of the reduced gradient method      620
Self-scaling methods      420
Semi-infinite nonlinear programming problems      235
Semi-strictly quasiconvex      139 141
Semidefinite cuts      683 737
Semidefinite matrices      756
Semidefinite programming      683 736 748
Sensitivity Analyses      26 256 533
Sensitivity to parameters and data      330
Separable nonlinear program      684
Separable programming      684
separate      53
Separating hyperplane      766
Separation of two convex sets      59
Separation of two sets      52
SEQUENCE      759 761
Sequential linear programming      568
Sequential programming approaches      576
Sequential search procedures      347
Sequential unconstrained minimization technique (SUMT)      484
Sets      759
Sherman — Morrison — Woodbury formula      419
Shifted/modified barrier method      534
Signomial programming problem      712
Signomials      712
simplex      43
Simplex method      75 76 456 652
Simplex tableau      80
Simultaneous search      346
Single-step procedure      434
Singular-value decomposition      755
Skew symmetric      746 753
Slack variable      77 81
Slater's constraint qualification      243 247
Soft constraints      28
Software description      653
Solid set      45 771
Solution      124
Solution procedure      317
Solution set      318
Space dilation      441 466
Spacer step      326 432
Spanning vectors      752
Spectral decomposition      752
Square root (of matrix)      755
Standard format      77
State vector      4
Statistical parameter estimation      36
Steepest ascent directions      283
Steepest descent algorithm      387
Steepest descent algorithm with affine scaling      394
Steepest descent method      384
Step bounds      568
Step length      441
Stochastic resource allocation      20
Straight-line directions      180
Strict complementary slackness condition      499
Strict containment      760
Strict convexity at $\bar{x}$      145
Strict local optimal solution      124
Strict Mangasarian — Fromovitz constraint qualification      255
Strict pseudoconvexity at $\bar{x}$      146
Strict quasiconvexity at $\bar{x}$      145
Strict unimodality      345
Strictly concave      98 767
Strictly convex      98 767 769
Strictly positive subdefinite      157
Strictly pseudoconcave      142
Strictly pseudoconvex      142 768
Strictly quasiconcave      139
Strictly quasiconvex      139 141 768
Strictly separate      53
Strictly unimodal      445
Strong duality result      85
Strong duality theorem      267 777
Strong local optimal solution      124
Strong quasiconvexity      140
Strong quasiconvexity at $\bar{x}$      146
Strong separation      54 61
Strongly active constraints      213
Strongly monotone      727
Strongly quasiconcave      141
Strongly quasiconvex      140 768
Strongly unimodal      156 445
Structural design      9
Subadditive      149
Subdifferential      105
Subgradient      105 103 279
Subgradient deflection      441
Subgradient optimization      435
Subhyperrectangles      679
Suboptimization strategy      622
subproblem      290 291
Subsequence      761
Subset      759
Successive linear programming approach      568 650
Successive quadratic programming approach      576 576 650
Sufficient Optimality Conditions      168
Sum map      334
Sum vector      751
Sup norm      334
Superbasic variables      621
Superdiagonalization algorithm      122
Superlinear      332
Superlinear convergence      331
Superlinearly convergent polynomial time primal-dual path-following methods      534
Support function      149
Support of sets at boundary points      57
Supporting hyperplane      57 58 766
Supporting hyperplane method      340
Supremum      760
Surrogate dual problem      313
Surrogate relaxation      232
symmetric      753
Tableau format of the simplex method      80
Tangential approximation      292
target value      443
Taylor series, first-order      109
Taylor series, second-order      112 113
Taylor's theorem      764
Terminating the algorithm      323
Three-point pattern      361 446 447
Three-term recurrence relationships      428
Tight constraints      177
Topkis — Veinott's modification of the feasible direction algorithm      561
Trajectory      4
Trajectory constraint function      5
Transportation problem      25
TRANSPOSE      753
Transposition      753
Triangularization      757
Truncated Newton methods      465
Trust region methods      398 400
Trust region parameter      400
Trust region restrictions      568
Trust region subproblem      400
Twice differentiable      112
Twice differentiable at $\bar{x}$      763
Two-bar truss      9
Unbounded      77
Unbounded-infeasible relationship      84
Unconstrained problems      166
Uniform search      346
Unimodal      156
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