Convex Analysis and Minimization Algorithms II: Advanced Theory and Bundle MethodsFrom the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience" |
Contents
II | 1 |
III | 2 |
IV | 9 |
VI | 15 |
VII | 24 |
IX | 27 |
X | 29 |
XI | 35 |
LXI | 170 |
LXII | 171 |
LXIII | 174 |
LXIV | 178 |
LXVI | 181 |
LXVII | 185 |
LXVIII | 190 |
LXIX | 195 |
XII | 37 |
XIII | 40 |
XIV | 42 |
XV | 47 |
XVI | 49 |
XVII | 54 |
XIX | 56 |
XX | 61 |
XXI | 65 |
XXII | 69 |
XXIII | 71 |
XXIV | 72 |
XXVI | 73 |
XXVII | 75 |
XXVIII | 76 |
XXIX | 79 |
XXXI | 82 |
XXXII | 91 |
XXXIII | 92 |
XXXIV | 95 |
XXXV | 98 |
XXXVI | 102 |
XXXVII | 106 |
XXXVIII | 110 |
XXXIX | 113 |
XLI | 116 |
XLII | 118 |
XLIII | 119 |
XLIV | 123 |
XLV | 125 |
XLVI | 127 |
XLVII | 129 |
XLVIII | 137 |
L | 141 |
LI | 147 |
LIII | 150 |
LIV | 154 |
LV | 157 |
LVI | 161 |
LVII | 162 |
LVIII | 165 |
LIX | 166 |
LX | 168 |
LXXI | 199 |
LXXII | 203 |
LXXIII | 206 |
LXXV | 209 |
LXXVI | 212 |
LXXVII | 216 |
LXXIX | 219 |
LXXX | 223 |
LXXXII | 227 |
LXXXIII | 233 |
LXXXIV | 236 |
LXXXV | 241 |
LXXXVI | 244 |
LXXXVII | 248 |
LXXXIX | 250 |
XC | 254 |
XCI | 263 |
XCIII | 266 |
XCIV | 268 |
XCV | 269 |
XCVI | 271 |
XCVII | 273 |
XCVIII | 275 |
C | 276 |
CI | 279 |
CII | 283 |
CIII | 285 |
CIV | 286 |
CV | 289 |
CVI | 292 |
CVII | 295 |
CVIII | 299 |
CIX | 301 |
CXI | 307 |
CXII | 314 |
CXIII | 317 |
CXV | 322 |
CXVI | 326 |
CXVII | 331 |
CXVIII | 337 |
345 | |
Other editions - View all
Convex Analysis and Minimization Algorithms I: Fundamentals Jean-Baptiste Hiriart-Urruty,Claude Lemarechal No preview available - 1996 |
Common terms and phrases
1-coercive affine function Algorithm Algorithm 1.6 approximate subdifferential assumption black box U1 bundle methods calculus rule Chap closed convex function compute conjugate consider constraints Conv convergence convex combination convex hull convex set Corollary cutting-plane decrease defined definition descent direction descent-step dɛ ƒ difference quotient differentiable dual function dual problem duality gap epi ƒ example f(x+td f(xk finite everywhere function ƒ ƒ xk gradient holds hyperplane implies inequality infimum Lagrange problem Lagrangian Lemma line-search linear loop to Step minimizing ƒ nonempty nonnegative norm notation null-step objective function obtain optimal primal problem PROOF Proposition quadratic quadratic function Remark result s₁ satisfying sequence Sk+1 solution solve stabilized stepsize stopping criterion subgradient Suppose Theorem variable xk+1 yk+1