1. 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

2. 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

3. Applications
Power minimization with piecewise linear power-delay curve [?]
l1 -norm minimization (c.f. [?, Ex. 7.18])
min ||x||1
s. 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