plq_me - Piecewise linear quadratic (plq), Moreau envelope

Calling Sequence

plqme = plq_me(plqf,lambda)

Parameters

• plqf : matrix. A plq function with dimensions n x 4.
• lambda : constant, smoothing parameter.
• plqme : matrix. A plq function with dimensions n x 4.

Description

Compute the Moreau envelope (ME) transform of a convex plq function, where the input and output is given in the form of a plq matrix. The Moreau Envelope is computed using the formula:

    M[lambda](s) = (1/2lambda)||s||^2 - (1/lambda)g*[lambda](s),
    where g[lambda](x) = (1/2)*||x||^2 + lambda*f(x),
      and * represents the Fenchel Conjugate.

Examples

lambda=1;
fctn = [%inf,1/2,0,0];
result = plq_me(fctn,lambda);
  

See Also

plq_function,  

Author

Mike Trienis, University of British Columbia, BC, Canada

Used Function