plq_pa - Piecewise linear quadratic (plq), convex proximal average via conjugates

Calling Sequence

pa = plq_pa(f1,f2,lambda_pa)

Parameters

• f1 : matrix. A plq function with dimensions n x 4.
• f2 : matrix. A plq function with dimensions n x 4.
• lambda_pa : constant. An intermediate function.
• pa : matrix. A plq function with dimensions n x 4.

Description

Compute the proximal average (PA) of two plq functions at a specified lambda_pa value. The PA is computed using the following formula, where * represents the Fenchel Conjugate.

    P(f1,lambda,f2) = [ (1 - lambda)(f1 + (1/2)||.||^2)* + lambda(f2 + (1/2)||.||^2)* ]* - (1/2)||.||^2

Examples

lambda_pa = 0.5;
f1 = [%inf, 0, 1, 0];
f2 = [%inf, 0, -1, 5]; 
result = plq_pa(f1, f2, lambda_pa);
  

See Also

plq_function,  

Author

Mike Trienis, University of British Columbia, BC, Canada