## Introduction to Global OptimizationIn this edition, the scope and character of the monograph did not change with respect to the first edition. Taking into account the rapid development of the field, we have, however, considerably enlarged its contents. Chapter 4 includes two additional sections 4.4 and 4.6 on theory and algorithms of D.C. Programming. Chapter 7, on Decomposition Algorithms in Nonconvex Optimization, is completely new. Besides this, we added several exercises and corrected errors and misprints in the first edition. We are grateful for valuable suggestions and comments that we received from several colleagues. R. Horst, P.M. Pardalos and N.V. Thoai March 2000 Preface to the First Edition Many recent advances in science, economics and engineering rely on nu merical techniques for computing globally optimal solutions to corresponding optimization problems. Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering. Due to the existence of multiple local optima that differ from the global solution all these problems cannot be solved by classical nonlinear programming techniques. During the past three decades, however, many new theoretical, algorith mic, and computational contributions have helped to solve globally multi extreme problems arising from important practical applications. |

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### Contents

III | 1 |

IV | 10 |

V | 16 |

VI | 20 |

VII | 25 |

VIII | 26 |

IX | 32 |

X | 34 |

LVI | 188 |

LVII | 195 |

LVIII | 196 |

LIX | 201 |

LXII | 202 |

LXIII | 203 |

LXIV | 204 |

LXV | 206 |

XI | 35 |

XII | 39 |

XIII | 49 |

XIV | 51 |

XV | 52 |

XVI | 56 |

XVII | 62 |

XVIII | 71 |

XIX | 74 |

XX | 79 |

XXI | 83 |

XXII | 86 |

XXIII | 87 |

XXIV | 88 |

XXV | 91 |

XXVI | 93 |

XXVII | 97 |

XXVIII | 101 |

XXIX | 109 |

XXX | 110 |

XXXII | 112 |

XXXIII | 118 |

XXXV | 119 |

XXXVI | 122 |

XXXVII | 123 |

XXXVIII | 129 |

XXXIX | 133 |

XL | 135 |

XLI | 136 |

XLII | 138 |

XLIII | 142 |

XLIV | 147 |

XLV | 149 |

XLVI | 154 |

XLVII | 157 |

XLVIII | 159 |

XLIX | 162 |

L | 163 |

LI | 165 |

LII | 171 |

LIII | 177 |

LIV | 181 |

LV | 182 |

LXVI | 210 |

LXVII | 211 |

LXVIII | 212 |

LXIX | 214 |

LXX | 219 |

LXXI | 224 |

LXXII | 233 |

LXXIII | 237 |

LXXIV | 240 |

LXXV | 241 |

LXXVI | 242 |

LXXVII | 243 |

LXXVIII | 247 |

LXXIX | 248 |

LXXX | 253 |

LXXXI | 255 |

LXXXII | 259 |

LXXXIII | 260 |

LXXXIV | 264 |

LXXXV | 267 |

LXXXVI | 270 |

LXXXVII | 271 |

LXXXVIII | 273 |

LXXXIX | 274 |

XC | 275 |

XCI | 276 |

XCIII | 278 |

XCIV | 285 |

XCV | 288 |

XCVI | 291 |

XCVII | 293 |

XCIX | 297 |

C | 299 |

CI | 301 |

CII | 305 |

CIII | 311 |

CIV | 313 |

CV | 316 |

CVI | 317 |

CVII | 341 |

349 | |

### Other editions - View all

Introduction to Global Optimization R. Horst,Panos M. Pardalos,Nguyen Van Thoai Limited preview - 1995 |

Introduction to Global Optimization R. Horst,Panos M. Pardalos,Nguyen Van Thoai Limited preview - 1995 |

### Common terms and phrases

7-extension affine function Algorithm 3.5 assume bound algorithm branch and bound Compute concave function concave minimization problem Consider constraints convergence convex combination convex envelope convex functions convex set corresponding d.c. functions d.c. program defined denote edge equivalent example feasible domain feasible point feasible set fi(x finite number function f(x G IRn gi(x given global minimum global optimization hence implies inequality integer intersection iteration Kuhn-Tucker linear program Lipschitz constant Lipschitzian lower bound matrix maximum clique problem MCCFP n-simplex node nonconvex nonempty nonlinear NP-complete NP-hard objective function objective function value obtain optimal solution optimal value optimization problem outer approximation Pardalos partition sets polynomial polytope Problem CDP programming problem Proof Proposition quadratic programming rectangle satisfying Section sequence simplex solution of Problem subdivision subproblem Theorem upper bound variables vector vertex vertex set vertices xTQx zero-one