Problem 524. Sequential Unconstrained Minimization (SUMT) using Interior Penalty

Write a function to find the values of a design variable vector, x, that minimizes a scalar objective function, f ( x ), given a function handle to f, and a starting guess, x0, subject to inequality constraints g ( x )<=0 with function handle g. Use a logarithmic interior penalty for the sequential unconstrained minimization technique (SUMT) with an optional input vector of increasing penalty parameter values. That is, the penalty (barrier) function, P, is

 P(x,r) = -sum(log(-g(x)))/r

where r is the penalty parameter.