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An interior algorithm for nonlinear optimization that combines line search and trust region steps

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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.

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These authors were supported by National Science Foundation grants CCR-9987818, ATM-0086579, and CCR-0219438 and Department of Energy grant DE-FG02-87ER25047-A004.

This author was supported by Asociación Mexicana de Cultura, A.C. and CONACyT grant 39372-A.

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Waltz, R., Morales, J., Nocedal, J. et al. An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Program. 107, 391–408 (2006).

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