Wednesday, 30 September 2009

geometry - Recovering a piecewise affine function

Lets say I have an piecewise affine convex function f(x1,x2), on which the following operations are possible:



  • Computing f(x1,x2).

  • Computing a subgradient to f at (x1,x2)

  • Computing all breakpoints along a line a1x1+a2x2=a3

What is an efficient algorithm to compute f completely, i.e. to compute all its breakpoints? Are there any general methods?

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