Convex Optimization.pdf

节选段落一：
Rockafellar, SIAM Review 1993
Zaborszky Lecture Series, September 18, 2006 7
Convex optimization
minimize f0(x)
subject to f1(x) ≤ 0, . . . , fm(x) ≤ 0
x ∈ Rn is optimization variable; fi : Rn → R are convex:
fi(λx + (1 − λ)y) ≤ λfi(x) + (1 − λ)fi(y)
for all x, y, 0 ≤ λ ≤ 1
• includes LS, LP, QP, and


节选段落二：
and extremely difficult
moral: very difficult and very easy problems can look quite similar
(to the untrained eye)
Zaborszky Lecture Series, September 18, 2006 11
Convex Analysis and Optimization
Convex analysis & optimization
nice properties of convex optimization problems known since 1960s
• local


节选段落三：
more expressive
• lots of applications still to be discovered
Zaborszky Lecture Series, September 18, 2006 46
Some references
• Convex Optimization, Boyd & Vandenberghe, 2004
www.stanford.edu/~boyd/cvxbook.html
• Introductory Lectures on Convex Optimization, Nesterov, 2003
• Lectures on Modern Convex