Practical Bilevel Optimization: Algorithms and ApplicationsThe focus of this book is on bilevel programming which combines elements of hierarchical optimization and game theory. The basic model addresses the problem where two decision-makers, each with their individual objectives, act and react in a noncooperative manner. The actions of one affect the choices and payoffs available to the other but neither player can completely dominate the other in the traditional sense. Over the last 20 years there has been a steady growth in research related to theory and solution methodologies for bilevel programming. This interest stems from the inherent complexity and consequent challenge of the underlying mathematics, as well as the applicability of the bilevel model to many real-world situations. The primary aim of this book is to provide a historical perspective on algorithmic development and to highlight those implementations that have proved to be the most efficient in their class. A corollary aim is to provide a sampling of applications in order to demonstrate the versatility of the basic model and the limitations of current technology. What is unique about this book is its comprehensive and integrated treatment of theory, algorithms and implementation issues. It is the first text that offers researchers and practitioners an elementary understanding of how to solve bilevel programs and a perspective on what success has been achieved in the field. Audience: Includes management scientists, operations researchers, industrial engineers, mathematicians and economists. |
From inside the book
Results 1-5 of 67
Page vii
... Computational Comparisons 222 6 LINEAR BLP : DISCRETE VARIABLES 232 6.1 Introduction 232 Properties of the Zero - One Linear BLPP 233 6.2.1 Reductions to Linear Three - Level Programs 237 6.2.2 Algorithmic Implications 244 6.3 ...
... Computational Comparisons 222 6 LINEAR BLP : DISCRETE VARIABLES 232 6.1 Introduction 232 Properties of the Zero - One Linear BLPP 233 6.2.1 Reductions to Linear Three - Level Programs 237 6.2.2 Algorithmic Implications 244 6.3 ...
Page viii
... Computational Experience 6.5.3 Assessment CONVEX BILEVEL PROGRAMMING 258 259 266 267 269 7.1 Introduction 269 7.2 Descent Approaches for the Quadratic BLPP 272 7.2.1 An EIR Point Descent Algorithm 274 7.2.2 A Modified Steepest Descent ...
... Computational Experience 6.5.3 Assessment CONVEX BILEVEL PROGRAMMING 258 259 266 267 269 7.1 Introduction 269 7.2 Descent Approaches for the Quadratic BLPP 272 7.2.1 An EIR Point Descent Algorithm 274 7.2.2 A Modified Steepest Descent ...
Page x
... Computational Results 449 12.5.1 Grid Search Solutions 449 12.5.2 Output from SQP 12.6 Discussion REFERENCES INDEX 450 452 455 469 PREFACE The use of optimization techniques has become integral to X PRACTICAL BILEVEL OPTIMIZATION.
... Computational Results 449 12.5.1 Grid Search Solutions 449 12.5.2 Output from SQP 12.6 Discussion REFERENCES INDEX 450 452 455 469 PREFACE The use of optimization techniques has become integral to X PRACTICAL BILEVEL OPTIMIZATION.
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Contents
III | 3 |
IV | 5 |
V | 8 |
VI | 10 |
VII | 11 |
VIII | 12 |
IX | 14 |
X | 17 |
XCIII | 250 |
XCIV | 254 |
XCV | 257 |
XCVI | 258 |
XCVII | 259 |
XCVIII | 266 |
XCIX | 267 |
C | 269 |
XII | 22 |
XIII | 23 |
XIV | 25 |
XV | 29 |
XVI | 30 |
XVII | 32 |
XVIII | 33 |
XIX | 37 |
XX | 41 |
XXI | 42 |
XXIII | 47 |
XXV | 48 |
XXVI | 49 |
XXVII | 51 |
XXIX | 54 |
XXX | 57 |
XXXI | 59 |
XXXII | 61 |
XXXIV | 66 |
XXXVI | 72 |
XXXVII | 76 |
XXXIX | 78 |
XL | 83 |
XLI | 87 |
XLII | 89 |
XLIII | 91 |
XLIV | 92 |
XLV | 96 |
XLVI | 102 |
XLVII | 106 |
XLVIII | 109 |
XLIX | 110 |
L | 114 |
LI | 118 |
LII | 121 |
LIII | 127 |
LV | 130 |
LVI | 133 |
LVII | 137 |
LVIII | 140 |
LIX | 142 |
LX | 143 |
LXI | 155 |
LXII | 156 |
LXIII | 157 |
LXIV | 159 |
LXV | 164 |
LXVI | 167 |
LXVII | 169 |
LXVIII | 170 |
LXIX | 175 |
LXX | 181 |
LXXII | 185 |
LXXIII | 188 |
LXXIV | 193 |
LXXV | 195 |
LXXVII | 198 |
LXXVIII | 202 |
LXXIX | 203 |
LXXX | 204 |
LXXXI | 209 |
LXXXII | 213 |
LXXXIII | 218 |
LXXXIV | 222 |
LXXXV | 232 |
LXXXVI | 233 |
LXXXVII | 237 |
LXXXVIII | 244 |
LXXXIX | 245 |
XC | 247 |
XCI | 248 |
XCII | 249 |
CI | 272 |
CII | 274 |
CIII | 276 |
CIV | 283 |
CV | 284 |
CVI | 290 |
CVII | 291 |
CVIII | 296 |
CIX | 301 |
CX | 305 |
CXI | 309 |
CXII | 311 |
CXIII | 320 |
CXIV | 327 |
CXV | 332 |
CXVI | 333 |
CXVII | 335 |
CXVIII | 339 |
CXIX | 341 |
CXX | 344 |
CXXI | 347 |
CXXII | 352 |
CXXIII | 359 |
CXXIV | 361 |
CXXV | 362 |
CXXVI | 363 |
CXXVII | 364 |
CXXVIII | 369 |
CXXIX | 370 |
CXXX | 373 |
CXXXI | 374 |
CXXXII | 375 |
CXXXIV | 376 |
CXXXV | 378 |
CXXXVI | 381 |
CXXXVII | 386 |
CXXXVIII | 389 |
CXXXIX | 391 |
CXL | 392 |
CXLI | 394 |
CXLII | 395 |
CXLIII | 397 |
CXLIV | 399 |
CXLV | 402 |
CXLVI | 403 |
CXLVII | 405 |
CXLVIII | 407 |
CXLIX | 410 |
CL | 412 |
CLI | 414 |
CLII | 415 |
CLIV | 418 |
CLV | 419 |
CLVI | 423 |
CLVII | 424 |
CLVIII | 425 |
CLIX | 426 |
CLX | 428 |
CLXI | 430 |
CLXII | 434 |
CLXIII | 435 |
CLXV | 436 |
CLXVI | 439 |
CLXVII | 440 |
CLXIX | 443 |
CLXX | 446 |
CLXXI | 449 |
CLXXIII | 450 |
CLXXIV | 452 |
455 | |
469 | |
Other editions - View all
Practical Bilevel Optimization: Algorithms and Applications Jonathan F. Bard No preview available - 2010 |
Common terms and phrases
algorithm assumed b₁ b₂ backtracking bilevel programming biofuel branch and bound c₁x coefficients column complementary slackness computational consider constraints convergence convex convex combination convex functions corresponding cost decision variables defined denoted descent dual equivalent example exists extreme points fathomed feasible region feasible solution finite follower's problem formulation GABBA given global optimum go to Step implies inducible region inequality infeasible iteration Kuhn-Tucker leader linear BLPP linear program linearly independent live nodes lower bound lower-level problem matrix minimize mixed-integer nonbasic variables nonfood crop nonlinear programming nonnegative objective function objective function value obtained optimal solution optimization problems parameter partition penalty pivot primal procedure programming problem Proposition quadratic rational relaxation satisfying search tree Section sequence simplex algorithm simplex method slack variable solve subject to G(x subproblem Table tableau Theorem upper bound vector zero
Popular passages
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