ON THE GOLDSTEIN-LEVITIN-POLYAK GRADIENT PROJECTION METHOD.

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3 Scopus citations

Abstract

This paper considers some aspects of a gradient projection method proposed by A. Goldstein, E. Levitin and B. Polyak and more recently, in a less general context, by G. McCormick. Some convergent stepsize rules to be used in conjunction with the method are proposed and analyzed. These rules are similar in spirit with the efficient L. Armijo rule for the method of steepest descent and under mild assumptions they have the desirable property that they identify the set of active inequality constraints in a finite number of iterations. As a result the method may be converted towards the end of the process to a conjugate direction, Quasi-Newton or Newton's method and achieve the attendant superlinear convergence rate. A quadratically convergent combination of the method with Newton's method is proposed as an example. Such combined methods appear to be very efficient for large scale problems with many simple constraints such as those often appearing in optimal control.

Original languageEnglish (US)
Pages47-52
Number of pages6
DOIs
StatePublished - 1974
Externally publishedYes
EventIEEE Conf on Decis and Control, 1974, incl Symp on Adapt Processes, 13th, Proc, Nov 20-22 1974 - Phoenix, AZ, USA
Duration: Nov 20 1974Nov 22 1974

Conference

ConferenceIEEE Conf on Decis and Control, 1974, incl Symp on Adapt Processes, 13th, Proc, Nov 20-22 1974
CityPhoenix, AZ, USA
Period11/20/7411/22/74

ASJC Scopus subject areas

  • Engineering(all)

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