You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: mat_dual.m
    path of file: ./repos/CS_MoCo_LAB/reconstruction/matlab/CS_LAB_matlab/utils/utils_SLEP/SLEP/functions/trace
    
    the code of the file until where you have to start completion: % revised on September 21, 2010 by Shuiwang Ji to make parameters consistent

% March 29 2009
% written by T. K. Pong and P. Tseng
%
% This Matlab function solves
%   min_{W} f(W) = 1/2*\|A*W-Y\|^2_F+\|W\|_*,
% where A is p by n and Y is p by m (so W is n by m), and
% \|\|_* is the nuclear norm.
% The code requires that p>=m.
% 
% This code first reduces A to have full row rank.  Then it
% applies a feasible descent method to solve the dual
% problem:
%   min_U 1/2*<C,U*U'> + <E',U>  s.t.   U'*U <= I, 
% where C=(A'*A)^{-1} and E=Y'*A*C (so U is m by n
    
function solves
%   min_{W} f(W) = 1/2*\|A*W-Y\|^2_F+\|W\|_*,
% where A is p by n and Y is p by m (so W is n by m), and
% \|\|_* is the nuclear norm.
% The code requires that p>=m.
% 
% This code first reduces A to have full row rank.  Then it
% applies a feasible descent method to solve the dual
% problem:
%   min_U 1/2*<C,U*U'> + <E',U>  s.t.   U'*U <= I, 
% where C=(A'*A)^{-1} and E=Y'*A*C (so U is m by n).
% From the solution U we obtain  W = E'+C*U'.
%
% This matlab function can be called using the command
%
% [W,fmin] = mat_dual(A,Y,lambda,opt);
%
% Input:
% A,Y are as described above.
% lambda: regularization parameter
% opt.alg    = 1  Frank-Wolfe method with line search 
%              2  gradient-projection method with large constant stepsize + line search
%              3  Accelerated grad-proj method with small constant stepsize
% opt.tol    = termination tolerance (e.g., 1e-3).
% opt.freq   = frequency of termination checks (e.g., n or 10).
%
% Output: 
% W  = the optimal solution
% pobj   = optimal objective function value of the original problem.

function [W,pobj] = mat_dual(A,Y,lambda,opt)

B = Y;
clear Y;

if nargin<4
    opt = [];
end