<< plq_gph plq plq_isConvex >>

CCA (Computational Convex Analysis) >> plq > plq_infconv_lft

plq_infconv_lft

Piecewise linear quadratic (plq), Inf-convolution (via LFT)

Calling Sequence

plqic = plq_infconv_lft(plqf, plqg)

Parameters

plqf

matrix. A PLQ function.

plqg

matrix. A PLQ function.

plqic

matrix. The PLQ function that is the inf-convolution of plqf and plqg.

Description

Computes the infimal convolution (or epi-addition) of two convex PLQ functions. The inf-convolution is defined by the formula

When f and g are convex (and proper, lower-semicontinuous), we rewrite the inf-convolution in terms of the Legendre-Frenchel conjugate (denoted by *),

This inf-convolution is also a PLQ function. This algorithm runs in O(n + m) time, where n and m are the size of f and g, respectively.

Examples

plqf = [-1,0,-1,0; 1,0,0,1; %inf,0,1,0];
plqg = [%inf,1,2,1];
plqic = plq_infconv_lft(plqf, plqg),
plq_plotMultiple(-4, 3, plqf, plqg, plqic);
xtitle("PLQ Convex Inf-convolution");
legend(["f", "g", "f ic g"]);

See Also

Authors

Bryan Gardiner, University of British Columbia, BC, Canada


Report an issue
<< plq_gph plq plq_isConvex >>