The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests. Key words: constrained optimization, interior point method, large-scale optimization, nonlinear programming, primal method, primal-dual method, successive quadratic programming, trust region method.

Jorge Nocedal z We study the local convergence of a primal-dual interior point method for nonlinear programming. A linearly convergent version of this algorithm has been shown in [2] to be capable of solving large and di cult non-convex problems. But for the algorithm to reach its full potential, it must converge rapidly to the solution. In this paper we describe how to design the algorithm so that it converges superlinearly on regular problems. Key words: constrained optimization, interior point method, large-scale optimization, nonlinear programming, primal method, primal-dual method, successive quadratic programming.

A modified Cholesky factorization algorithm introduced originally by Gill and Murray and refined by Gill, Murray and Wright, is used extensively in optimization algorithms. Since its introduction in 1990, a di#erent modified Cholesky factorization of Schnabel and Eskow has also gained widespread usage. Compared with the Gill-Murray-Wright algorithm, the Schnabel-Eskow algorithm has a smaller a priori bound on the perturbation added to ensure positive definiteness, and some computational advantages, especially for large problems. Users of the Schnabel-Eskow algorithm, however, have reported cases from two di#erent contexts where it makes a far larger modification to the original matrix than is necessary and than is made by the Gill-Murray-Wright method. This paper reports a simple modification to the Schnabel-Eskow algorithm that appears to correct all the known computational di#culties with the method, without harming its theoretical properties, or its computational behavior in any ot...

This paper addresses the local convergence properties of the ane-scaling interior-point algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interiorpoint scheme and the size of the residual of the linear system that provides the step direction. The analysis follows the classical theory for quasi-Newton methods and addresses q-linear, qsuperlinear, and q-quadratic rates of convergence.