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Nonlinear programming: A quadratic analysis of ridge paralysis

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Abstract

The numerical solution of nonlinear programming problems by first-order techniques, such as gradient projection techniques, is difficult when ridges are encountered. Ridges are described and analyzed. Second-order information about the augmented objective function, properly used, can yield a search direction that moves along a ridge, even in the constrained case. The analysis applies to situations in which the objective function (maximization) is not necessarily concave and the constraint functions (G j ⩽ 0) are not necessarily convex.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computing Science, Washington University, St. Louis, Missouri

    Philip B. Zwart (Assistant Professor)

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  1. Philip B. Zwart
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Communicated by R. H. Howard

This research was supported in part by the Atomic Energy Commission under Research Contract No. A(11-1)-1493 and by the Department of Defense under Themis Grant No. F44620-69-C-0116.

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Zwart, P.B. Nonlinear programming: A quadratic analysis of ridge paralysis. J Optim Theory Appl 6, 331–339 (1970). https://doi.org/10.1007/BF00925381

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  • DOI: https://doi.org/10.1007/BF00925381

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