## 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

analysis Applications assumption BILD bilevel linear programming bilevel programming problem bilinear biofuel branch and bound complementarity problem computational concave consider constraints continuous mapping convergence convex function convex program Corollary corresponding decomposition defined denote equilibrium ethanol exists feasible set feasible solution FF/hl finite FMRP formulation given Global Optimization gradient interface iteration Journal of Global l)-level leader LICQ linear bilevel programming linear maxmin Lipschitz continuous lower level problem lower semicontinuous mapping f Mathematical Programming matrix method Migdalas minimum monotone MPEC multi-level programming multilevel optimization nonconvex nonfood crop nonlinear programming nonsmooth objective function obtained Operations Research optimal solution optimal value optimality conditions optimization problem parametric player polyhedron polynomial polynomial hierarchy Proof Proposition PSQP reformulation resp respect reverse convex satisfied Section sequence sequential quadratic programming set-valued solution algorithm solvable solve Step structure subproblems subset Theorem tion variational inequalities vector vertex