"An Interior Algorithm for Nonlinear Optimization that Combines Line Search and Trust Region Steps"
J.L. Morales, J. Nocedal, D. Orban, R. Waltz.
Mathematical Programming A, Vol. 102, pp. 391-408 (2006).
An interior-point method for nonlinear programming is presented. It enjoys the flexibility of switching between a line search method that computes steps by factoring the primal-dual equations and a trust region method that uses a conjugate gradient iteration. Steps computed by direct factorization are always tried first, but if they are deemed ineffective, a trust region iteration that guarantees progress toward stationarity is invoked. To demonstrate its effectiveness, the algorithm is implemented in the Knitro [6, 28] software package and is extensively tested on a wide selection of test problems.