## Convex OptimizationConvex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics. |

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### Contents

LXII | 397 |

LXIII | 402 |

LXIV | 405 |

LXV | 410 |

LXVI | 416 |

LXVII | 422 |

LXVIII | 432 |

LXIX | 438 |

21 | |

27 | |

XIII | 35 |

XIV | 43 |

XV | 46 |

XVI | 51 |

XVII | 59 |

XVIII | 60 |

XIX | 67 |

XX | 79 |

XXI | 90 |

XXII | 95 |

XXIII | 104 |

XXIV | 108 |

XXV | 112 |

XXVI | 113 |

XXVII | 127 |

XXVIII | 136 |

XXIX | 146 |

XXX | 152 |

XXXI | 160 |

XXXII | 167 |

XXXIII | 174 |

XXXIV | 188 |

XXXV | 189 |

XXXVI | 215 |

XXXVII | 223 |

XXXVIII | 232 |

XXXIX | 237 |

XL | 241 |

XLI | 249 |

XLII | 253 |

XLIII | 258 |

XLIV | 264 |

XLV | 272 |

XLVI | 273 |

XLVII | 289 |

XLVIII | 291 |

XLIX | 302 |

L | 305 |

LI | 318 |

LII | 324 |

LIII | 343 |

LIV | 344 |

LV | 351 |

LVI | 359 |

LVII | 364 |

LVIII | 374 |

LIX | 384 |

LX | 392 |

LXI | 393 |

LXX | 446 |

LXXI | 447 |

LXXII | 455 |

LXXIII | 457 |

LXXIV | 463 |

LXXV | 466 |

LXXVI | 475 |

LXXVII | 484 |

LXXVIII | 496 |

LXXIX | 508 |

LXXX | 513 |

LXXXI | 514 |

LXXXII | 521 |

LXXXIII | 525 |

LXXXIV | 531 |

LXXXV | 542 |

LXXXVI | 556 |

LXXXVII | 557 |

LXXXVIII | 561 |

LXXXIX | 562 |

XC | 568 |

XCI | 579 |

XCII | 585 |

XCIII | 596 |

XCIV | 609 |

XCV | 615 |

XCVI | 621 |

XCVII | 623 |

XCVIII | 631 |

XCIX | 633 |

C | 637 |

CI | 639 |

CII | 640 |

CIII | 645 |

CIV | 652 |

CV | 653 |

CVI | 655 |

CVII | 656 |

CVIII | 657 |

659 | |

CX | 661 |

CXI | 664 |

CXII | 668 |

CXIII | 672 |

CXIV | 681 |

684 | |

685 | |

CXVII | 697 |

701 | |

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### Common terms and phrases

affine function algorithm analytic center approximation problem assume Axnt backtracking line search barrier method Cholesky factorization concave concave function condition number cone consider constraint functions convergence convex function convex optimization problem convex set cost defined denote detector dual feasible dual function dual problem duality gap eigenvalue ellipsoid equality constraints Euclidean example expressed feasible point Figure flops G Rn geometric given gradient Hessian hyperplane inequality constraint infeasible start Newton interior-point methods interpretation iterations Lagrange dual least-squares problem line search linear equations linear inequalities linear programming log-concave logarithm lower bound matrix maximize maximum Newton's method nonnegative nonzero norm number of Newton objective function optimal point optimal value parameter Pareto optimal penalty function polyhedron polynomial primal problem minimize proper cone quadratic quasiconvex quasiconvex function residual satisfies scalar Schur complement Show solution solve strong duality subject to Ax subject to fi(x sublevel sets Suppose zero