### Jacek Gondzio (University of Edinburgh)

#### Interior point methods for optimization: just call Newton, Lagrange and Fiacco & McCormick

*Wednesday 11 November 1998 at 15.30, JCMB 6324*

##### Abstract

Following [1], to derive the primal-dual interior point algorithm one
should:

- replace nonnegativity constraints on the variables with logarithmic barrier
penalty terms;
- move equality constraints to the objective with the Lagrange
transformation to obtain an unconstrained optimization problem and write
first order optimality conditions for it;
- apply Newton's method to solve these first order optimality conditions
(i.e. to solve a system of nonlinear equations).

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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