Following [1], to derive the primal-dual interior point algorithm one should:
We shall do this exercise. Next, we shell focus on the computational aspects of interior point methods for linear, quadratic and general, nonlinear optimization.
[1] R. E. Marsten, R. Subramaniam, M. J. Saltzman, I. J. Lustig and D. F. Shanno, Interior point methods for linear programming: Just call Newton, Lagrange, and Fiacco and McCormick, Interfaces 20 (1990) No 4, pp 105-116.
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