## A Globally Convergent Interior Point Algorithm for General Non-Linear Programming
Problems

### Ioannis Akrotirianakis and Berc Rustem

This paper presents a primal-dual interior point algorithm for solving general
constrained non-linear programming problems. The initial problem is transformed to an
equivalent equality constrained problem, with inequality constraints incorporated into the
objective function by means of a logarithmic barrier function. Satisfaction of the
equality constraints is enforced through the incorporation of an adaptive quadratic
penalty function into the objective. The penalty parameter is determined using a strategy
that ensures a descent property for a merit function. It is shown that the adaptive
penalty does not grow indefinitely. The algorithm applies Newton's method to solve the
first order optimality conditions of the equivalent equality problem. Global convergence
of the algorithm is achieved through the monotonic decrease of a merit function. Locally
the algorithm is shown to be quadratically convergent.

Technical Report 97/14, (November 1997), Department of Computing, Imperial College of
Science, Technology and Medicine, 180 Queen's Gate, London SW7 2BZ, UK.

Contact: ia4@doc.ic.ac.uk