## Multilevel Optimization: Algorithms and ApplicationsA. Migdalas, Panos M. Pardalos, Peter Värbrand In many decision processes there is an hierarchy of decision-makers and decisions are taken at different levels in this hierarchy. Multilevel programming focuses on the whole hierarchy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of optimization problems which must be solved in a predetermined sequence. The field of multilevel optimization has become a well-known and important research field. Hierarchical structures can be found in scientific disciplines such as environment, ecology, biology, chemical engineering, mechanics, classification theory, databases, network design, transportation, game theory and economics. Moreover, new applications are constantly being introduced. This has stimulated the development of new theory and efficient algorithms. This volume contains 16 chapters written by various leading researchers and presents a cohesive authoritative overview of developments and applications in their emerging field of optimization. Audience: Researchers whose work involves the application of mathematical programming and optimization to hierarchical structures. |

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### Contents

II | 1 |

III | 2 |

IV | 3 |

V | 9 |

VI | 12 |

VII | 18 |

VIII | 23 |

IX | 24 |

LII | 186 |

LIII | 191 |

LIV | 195 |

LV | 209 |

LVI | 211 |

LVII | 213 |

LVIII | 218 |

LIX | 222 |

X | 25 |

XI | 29 |

XII | 36 |

XIII | 41 |

XIV | 51 |

XV | 54 |

XVI | 59 |

XVII | 61 |

XVIII | 63 |

XIX | 67 |

XX | 69 |

XXI | 76 |

XXII | 82 |

XXIII | 91 |

XXIV | 92 |

XXV | 95 |

XXVI | 101 |

XXVII | 103 |

XXVIII | 112 |

XXX | 117 |

XXXI | 118 |

XXXII | 119 |

XXXIII | 122 |

XXXIV | 133 |

XXXV | 137 |

XXXVII | 149 |

XXXVIII | 150 |

XXXIX | 153 |

XL | 155 |

XLI | 157 |

XLII | 159 |

XLIII | 160 |

XLIV | 165 |

XLV | 167 |

XLVI | 171 |

XLVII | 175 |

XLVIII | 176 |

XLIX | 177 |

LI | 181 |

LX | 228 |

LXI | 231 |

LXII | 233 |

LXIII | 235 |

LXIV | 240 |

LXV | 241 |

LXVI | 251 |

LXVII | 253 |

LXVIII | 257 |

LXIX | 263 |

LXX | 268 |

LXXI | 273 |

LXXII | 295 |

LXXIII | 297 |

LXXIV | 299 |

LXXV | 300 |

LXXVI | 304 |

LXXVII | 315 |

LXXVIII | 318 |

LXXIX | 322 |

LXXX | 327 |

LXXXI | 330 |

LXXXII | 333 |

LXXXIII | 336 |

LXXXIV | 340 |

LXXXV | 347 |

LXXXVI | 351 |

LXXXVII | 357 |

358 | |

LXXXIX | 359 |

XC | 361 |

XCI | 364 |

XCII | 367 |

XCIII | 370 |

XCIV | 373 |

XCV | 376 |

381 | |

### Other editions - View all

Multilevel Optimization: Algorithms and Applications A. Migdalas,Panos M. Pardalos,Peter Värbrand Limited preview - 2013 |

Multilevel Optimization: Algorithms and Applications A. Migdalas,Panos M. Pardalos,Peter Värbrand No preview available - 2011 |

### Common terms and phrases

algorithm analysis Applications approach assume assumption bilevel programming problem bounded called closed complementarity complexity computational consider constraints contains continuous convergence convex Corollary corresponding cost decision defined definition demand denote determined direction discussed elements energy equal equilibrium equivalent example exists farm feasible feasible solution Figure finite formulation given Global Optimization hence holds implies instance interface iteration Journal leader least linear programming mapping Mathematical Programming matrix mechanics method minimization multilevel nonconvex nonlinear Note objective function obtained Operations optimal solution optimal value optimization problem parametric player positive possible present Proof Proposition quadratic referred reformulation region Research respect satisfied sequence solution solve Step structure subproblems subset Theorem theory tion unique University variables vector vertex