Solve the portfolio QD problem using solvesdp and SeDuMi solver

solveportfolio.m

function [ opt, x_opt, diagnostics ] = solveportfolio( C, r, alpha )
%SOLVEPORTFOLIO Solve the portfolio problem.
%   Minizing the risk for investing in `n` different opportunities, while
%   keeping the expected return on investment above `alpha`.
%
%   This solves the following QD:
%
%      min  x' C x
%
%      st.  sum(x) = 1
%            r' x >= alpha
%               x >= 0

n = length(r);
x = sdpvar(n, 1);

% Set constraints.
F = set( r' * x >= alpha );
F = F + set( sum(x) == 1 );
F = F + set( x >= 0 );

% Minimum investment risk.
objective_function = x' * C * x;

% Solve optimization problem.
diagnostics = solvesdp(F, objective_function, ...
                       sdpsettings('showprogress', 1, 'solver', 'sedumi'));

% Cleanup return values.
opt = double(objective_function);
x_opt = double(x);
x_opt(x_opt < 1e-5) = 0;  % Truncate small values.

end