Globally Convergent Interior-Point Algorithm for Nonlinear Programming

This paper presents a primal-dual interior-point algorithm for solving general constrained nonlinear programming problems. The inequality constraints are incorporated into the objective function by means of a logarithmic barrier function. Also, satisfaction of the equality constraints is enforced through the use of an adaptive quadratic penalty function. The penalty parameter is determined using a strategy that ensures a descent property for a merit function. Global convergence of the algorithm is achieved through the monotonic decrease of a merit function. Finally, extensive computational results show that the algorithm can solve large and difficult problems in an efficient and robust way.Communicated by L. C. W. DixonThe research reported in this paper was done while the first author was at Imperial College. The authors gratefully acknowledge constructive comments from Professor L. C. W. Dixon and an anonymous referee. They are also grateful to Dr. Stanislav Zakovic for helpful suggestions and comments. Financial support was provided by EPSRC Grants M16016 and GR/G51377/01.