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
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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
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4Convexanalysis 78
.................. 78
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........................103
5 Special cases 113
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6 Nonsmooth optimization 143
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Nonsmooth regularity and strict differentiability . . . .....151
...........................158
...................167
7 The Karush-Kuhn-Tucker theorem 176
..............176
The Karush-Kuhn-Tucker theorem ...............184
........191
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8 Fixed points 204
’sfixedpoint