Write a function to find the values of a design variable vector, x, that minimizes a scalar objective function, f, given a function handle to f, a starting guess, x0, subject to inequality and equality constraints with function handles g<=0 and h=0, respectively. Use a quadratic exterior penalty for the sequential unconstrained minimization technique (SUMT) with an optional input vector of penalty parameter values that become increasingly larger.
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Please, be aware that test cases don't necessarily use all the same penalty parameters. For instance, I have used 1e6 for cases 2,3,4 & 6 and 1e4 for cases 1 & 5. It all depends on which method one uses for the exterior penalty (and approximations may fail because of it).
In a sense, it is like trying to find the secret formula instead of finding the minimum value of a function.