Methods for Constrained Optimization - MIT Certificate Error

I also ran the support vector machine method with a second order kernel function, whichproduces a quadratic decision function. The results are shown in Figure 12. We can seethat the penalty function method produces slightly different α values from quadraticprogramming due to the iteration cutoff error. The convergence criteria for the penalty8function method was set to . Making the convergence criteria tighter would help thepenalty function method to produce more accurate results, but would increase run-time.10 − x 1 x 2 l α3 5 +1 04 6 +1 02 2 +1 0.01087 4 +1 0.00179 8 +1 0-5 -2 –1 0.0070-8 2 –1 0-2 -9 –1 01 -4 –1 0.0055x 1 x 2 l α3 5 +1 04 6 +1 02 2 +1 0.01097 4 +1 0.00179 8 +1 0-5 -2 –1 0.0070-8 2 –1 0-2 -9 –1 01 -4 –1 0.0056x 1 x 2 l α3 5 +1 04 6 +1 02 2 +1 0.01097 4 +1 0.00179 8 +1 0-5 -2 –1 0.0070-8 2 –1 0-2 -9 –1 01 -4 –1 0.0056Figure 12. The second order decision function for example data is shown in green. Encircled are thesupport vectors. The data point values, labels, and optimal parameters α are shown on the right.