Graph-matrix calculus (GPH), Legendre-Fenchel conjugate
gphstar = gph_lft(gph)
matrix. A function in GPH matrix form.
matrix. The conjugate of the function gph, in GPH matrix form.
Computes the Legendre-Fenchel conjugate of a given GPH function. For a convex PLQ function f with GPH matrix [x;s;y], the GPH matrix of the conjuagte, f*, is
gph = [-1, 0, 0, 1, 2; .. -1, -1, 0, 0, 2; .. 1, 0, 0, 0, 1]; gphstar = gph_lft(gph), scf(); gph_plot(gph, gphstar); | ![]() | ![]() |
Bryan Gardiner
, University of British Columbia, BC, Canada