Lec05 convex pwl problems
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Lecture 5: Convex Piecewise Linear Problems
Wai-Shing Luk (陆伟成)
Fudan University
2012年 8月 13日
W.-S. Luk (Fudan Univ.) Lecture 5: Convex Piecewise Linear Problems 2012年 8月 13日 1 / 3
Remark 1
Can be reduced to problems with linear costs [?, p.239,p.260] by
modifying the underlying network.
Potential problem: partition the interval [d−(j), d+(j)] into
consecutive closed subintervals D1,D2, · · · ,Dr .
Flow problem: partition the interval [c−(j), c+(j)] into consecutive
closed subintervals C1,C2, · · · ,Cr .
W.-S. Luk (Fudan Univ.) Lecture 5: Convex Piecewise Linear Problems 2012年 8月 13日 2 / 3
Applications
Power minimization with piecewise linear power-delay curve [?]
l1-norm minimization (c.f. [?, Ex. 7.18])
min ||x ||1s. t. c− ≤ x ≤ c+,
AT x = b, b(V ) = 0
And hence, heuristics method for cardinality problems (c.f. EE364b
Boyd)
min card(x)
s. t. c− ≤ x ≤ c+,
AT x = b, b(V ) = 0
W.-S. Luk (Fudan Univ.) Lecture 5: Convex Piecewise Linear Problems 2012年 8月 13日 3 / 3