<< 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

- plq_deconv_lft
- plq_function

### Authors

`Bryan Gardiner`, University of British Columbia, BC, Canada

<< plq_gph | plq | plq_isConvex >>