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Interior-point methods for nonconvex nonlinear programming: Jamming and numerical testing

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Abstract.

The paper considers an example of Wächter and Biegler which is shown to converge to a nonstationary point for the standard primal–dual interior-point method for nonlinear programming. The reason for this failure is analyzed and a heuristic resolution is discussed. The paper then characterizes the performance of LOQO, a line-search interior-point code, on a large test set of nonlinear programming problems. Specific types of problems which can cause LOQO to fail are identified.

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Research of the first and third authors supported by NSF grant DMS-9870317, ONR grant N00014-98-1-0036.

Research of the second author supported by NSF grant DMS-9805495.

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Benson, H., Shanno, D. & Vanderbei, R. Interior-point methods for nonconvex nonlinear programming: Jamming and numerical testing. Math. Program., Ser. A 99, 35–48 (2004). https://doi.org/10.1007/s10107-003-0418-2

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