Convex Optimization, Teil 1Cambridge University Press, 08.03.2004 - 716 Seiten Convex 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. |
Inhalt
II | 1 |
IV | 4 |
V | 7 |
VI | 9 |
VII | 11 |
VIII | 14 |
IX | 16 |
X | 19 |
LXVI | 397 |
LXVII | 402 |
LXVIII | 405 |
LXIX | 410 |
LXX | 416 |
LXXI | 422 |
LXXII | 432 |
LXXIII | 438 |
XI | 21 |
XIII | 27 |
XIV | 35 |
XV | 43 |
XVI | 46 |
XVII | 51 |
XVIII | 59 |
XIX | 60 |
XX | 67 |
XXI | 79 |
XXII | 90 |
XXIII | 95 |
XXIV | 104 |
XXV | 108 |
XXVI | 112 |
XXVII | 113 |
XXVIII | 127 |
XXX | 136 |
XXXI | 146 |
XXXII | 152 |
XXXIII | 160 |
XXXIV | 167 |
XXXV | 174 |
XXXVI | 188 |
XXXVII | 189 |
XXXVIII | 215 |
XL | 223 |
XLI | 232 |
XLII | 237 |
XLIII | 241 |
XLIV | 249 |
XLV | 253 |
XLVI | 258 |
XLVII | 264 |
XLVIII | 272 |
XLIX | 273 |
L | 289 |
LI | 291 |
LIII | 302 |
LIV | 305 |
LV | 318 |
LVI | 324 |
LVII | 343 |
LVIII | 344 |
LIX | 351 |
LX | 359 |
LXI | 364 |
LXII | 374 |
LXIII | 384 |
LXIV | 392 |
LXV | 393 |
LXXIV | 446 |
LXXV | 447 |
LXXVI | 455 |
LXXVII | 457 |
LXXIX | 463 |
LXXX | 466 |
LXXXI | 475 |
LXXXII | 484 |
LXXXIII | 496 |
LXXXIV | 508 |
LXXXV | 513 |
LXXXVI | 514 |
LXXXVII | 521 |
LXXXVIII | 525 |
LXXXIX | 531 |
XC | 542 |
XCI | 556 |
XCII | 557 |
XCIII | 561 |
XCV | 562 |
XCVI | 568 |
XCVII | 579 |
XCVIII | 585 |
XCIX | 596 |
C | 609 |
CI | 615 |
CII | 621 |
CIII | 623 |
CIV | 631 |
CV | 633 |
CVI | 637 |
CVII | 639 |
CVIII | 640 |
CIX | 645 |
CX | 652 |
CXI | 653 |
CXII | 655 |
CXIII | 656 |
CXIV | 657 |
659 | |
CXVI | 661 |
CXVII | 664 |
CXVIII | 668 |
CXIX | 672 |
CXX | 681 |
684 | |
685 | |
CXXIII | 697 |
701 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
affine function algorithm analytic center approximation problem assume backtracking line search barrier method compute concave concave function condition number cone consider constraint functions convergence convex function convex optimization convex optimization problem convex set cost defined denote dual feasible dual function dual problem duality gap eigenvalue ellipsoid equality constraints Euclidean example expressed feasible point fi(x Figure flops fo(x function f geometric given gradient hyperplane inequality constraint infeasible start Newton interpretation iterations Lagrange dual least-squares problem line search linear equations linear inequalities linear programming log-concave logarithm lower bound matrix maximize maximum minimize subject Newton's method nonnegative norm number of Newton optimal point optimal value parameter Pareto optimal penalty function polynomial primal problem minimize quadratic quasiconvex quasiconvex function residual Rmxn satisfies scalar Schur complement self-concordant Show solution solve strong duality subject to Ax sublevel sets Suppose zero
Verweise auf dieses Buch
Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators Lloyd N. Trefethen,Mark Embree Eingeschränkte Leseprobe - 2005 |
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis Eingeschränkte Leseprobe - 2005 |