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Linearized ridge-path method for function minimization

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A modification based on a linearization of a ridge-path optimization method is presented. The linearized ridge-path method is a nongradient, conjugate direction method which converges quadratically in half the number of search directions required for Powell's method of conjugate directions. The ridge-path method and its modification are compared with some basic algorithms, namely, univariate method, steepest descent method, Powell's conjugate direction method, conjugate gradient method, and variable-metric method. The assessment indicates that the ridge-path method, with modifications, could present a promising technique for optimization.

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This work was in partial fulfillment of the requirements for the MS degree of the first author at Cairo University, Cairo, Egypt. The authors would like to acknowledge the helpful and constructive suggestions of the reviewer.

Communicated by H. Y. Huang

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TElzoughby, A.A., Metwalli, S.M. & Shawki, G.S.A. Linearized ridge-path method for function minimization. J Optim Theory Appl 30, 161–179 (1980). https://doi.org/10.1007/BF00934494

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Key Words

  • Optimization techniques
  • nonlinear programming
  • direct methods
  • numerical methods
  • conjugate directions
  • nongradient methods
  • ridge-path methods