Borweinjm Lewisas 2000 Convex Analysis N Nonlinear Optimization Theory N Examples Springer.pdf

文档介绍：CONVEX ANALYSIS AND NONLINEAR
OPTIMIZATION
Theory and Examples
JONATHAN M. BORWEIN
Centre for Experimental and Constructive Mathematics
Department of Mathematics and Statistics
Simon Fraser University, Burnaby, ., Canada V5A 1S6
******@
/∼jborwein
and
ADRIAN S. LEWIS
Department binatorics and Optimization
University of Waterloo, Waterloo, Ont., Canada N2L 3G1
******@
/∼aslewis
To our families
2
Contents
............................... 5
1 Background 7
......................... 7
........................ 16
2 Inequality constraints 22
....................... 22
................... 30
-functionsandfirstorderconditions............ 36
3 Fenchel duality 42
Subgradients and convex functions ............... 42
........................ 54
...................... 61
4Convexanalysis 78
.................. 78
....................... 90
........................103
5 Special cases 113
..............113
.....................120
........126
......................132
6 Nonsmooth optimization 143
......................143
3
Nonsmooth regularity and strict differentiability . . . .....151
...........................158
...................167
7 The Karush-Kuhn-Tucker theorem 176
..............176
The Karush-Kuhn-Tucker theorem ...............184
........191
.....................197
8 Fixed points 204
’sfixedpoint