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Nonlinear programming the choice of direction by gradient projection

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  • Philip B. Zwart

Abstract

Rosen's method of Gradient Projection chooses a search direction which is not necessarily the direction of steepest ascent. However, the projection of the gradient onto a “suitably chosen subspace” does yield the direction of steepest ascent. The suitable choice is easily recognized as a result of some theorems relating gradient projection to steepest ascent. These results lead to a modification of Rosen's method. The modification improves the choice of search direction and usually yields the steepest ascent direction without solving a quadratic programming problem.

Suggested Citation

  • Philip B. Zwart, 1970. "Nonlinear programming the choice of direction by gradient projection," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 17(4), pages 431-438, December.
    • Handle: RePEc:wly:navlog:v:17:y:1970:i:4:p:431-438
    DOI: 10.1002/nav.3800170403
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    Cited by:

    1. Honggang Wang, 2017. "Subspace dynamic‐simplex linear interpolation search for mixed‐integer black‐box optimization problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 305-322, June.

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