文档介绍：Corrections for the book CONVEX ANALYSIS AND OPTI-
MIZATION, Athena Scientific, 2003, by Dimitri P. Bertsekas
Last Changed: 5/3/04
p. 3 (+22) Change “as the union of the closures of all line segments” to
“as the closure of the union of all line segments”
p. 37 (-2) Change “Every x” to “Every x =0”
p. 38 (+1) Change “Every x in” to “Every x/∈ X that belongs to”
n
p. 38 (+19) Change “.,” to “with x1,...,xm ∈ and m ≥ 2, .,”
p. 63 (+4, +6, +7, +19) Change four times “cy”to“ay”
p. 67 (+3) Change “y ∈ AC”to“y ∈ AC”
p. 70 (+9) Change “[BeN02]” to “[NeB02]”
p. 110 (+3 after the figure caption) Change “... does not belong to
the interior of C” to “... does not belong to the interior of C and hence
does not belong to the interior of cl(C) [cf. Prop. (b)]”
p. 148 (-8) Change “ x | r(x) ≤γ”to“ z | r(z) ≤γ”
p. 213 (-6) Change “remaining vectors vj, j = i.” to “vectors vj with
vj = vi.”
n
p. 219 (+3) Change “fi : C →”to“fi : →”
p. 265 (+10) Change “d/d”to“−d/d”
p. 268 (-3) Change “j ∈ A(x∗)” to “j/∈ A(x∗)”
p. 338 (+17) Change “Section ” to “Section ”
p. 384 (+6) Change “convex, possibly nonsmooth functions” to “smooth
functions, and convex (possibly nonsmooth) functions”
p. 446 (+6 and +8) Interchange “... constrained problem ()” and
“... penalized problem ()”
p. 458 (+13) Change “... as well real-valued” to “... as well as real-
valued”
p. 458 (-10) Change “We will focus on this ... dual functions.” to “In
this case, the dual problem can be solved using gradient-like algorithms for
differentiable optimization (see ., Bertsekas [Ber99a]).”
1
Convex Analysis and
Optimization
Chapter 1 Solutions
Dimitri P. Bertsekas
with
Angelia Nedi´c and Asuman E. Ozdaglar
Massachusetts Institute of Technology
Athena Scientific, Belmont, Massachusetts
LAST UPDATE March 24, 2004
CHAPTER 1: SOLUTION MANUAL
Assume that C is convex. Then, clearly (λ1 + λ2)C ⊂λ1C + λ2C; this is true
even if C