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A parallel quasi-Newton algorithm for unconstrained optimization

Ein paralleles Quasi-Newton-Verfahren für unrestringierte Optimierungsaufgaben

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Abstract

In this paper, we present an asynchronous parallel quasi-Newton method. We assume that we havep+q processors, which are divided into two groups, the two groups execute in an asynchronous parallel fashion. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss the global and superlinear convergence of the parallel BFGS method. Finally we show numerical results of this algorithm.

Zusammenfassung

Dieser Beitrag stellt ein asynchron paralleles Quasi-Newton-Verfahren vor. Wir setzen voraus, daß esp+q Prozessoren gibt, die in zwei Gruppen geteilt sind. Die beiden Gruppen arbeiten asynchron parallel. Wenn die Zielfunktion zweimal stetig differenzierbar und gleichmäßig konvex ist, beweisen wir, daß die vom Verfahren erzeugte Iterationsfolge zur Optimallösung global und superlinear konvergiert.

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References

  1. Byrd, R. H., Nocedal, J.: A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM J. Numer. Anal.26, 727–739, (1989).

    Article  Google Scholar 

  2. Byrd, R. H., Nocedal, J., Yuan, Y.: Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal.24, 1171–1189 (1989).

    Article  Google Scholar 

  3. Dennis, J. E., Moré, J. J.: A characterization of superlinear convergence and its application to quasi-Newton methods. Math. Comput.28, 549–560 (1974).

    Google Scholar 

  4. Pardalos, P. M., Phillips, A. T., Rosen, J. B.: Topics in parallel computing in mathematical programming. New York: Science Press 1993.

    Google Scholar 

  5. Griewank, A., Toint, Ph L.: Local convergence analysis for partitioned quasi-Newton updates. Numer. Math.39, 429–448 (1982).

    Article  Google Scholar 

  6. Pearson, J. D.: Variable metric methods of minimization. Comput. J.12, 171–178 (1969).

    Article  Google Scholar 

  7. Powell, M. J. D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Nonlinear programming, SIAM-AMS Proceedings, vol. 9 (Cottle, R. W., eds.). Americal Mathematical Society, Providence, RI, 1976.

    Google Scholar 

  8. Chen, Z. Fei, P.: A parallel algorithm for constrained optimization problems. J. Comp. Appl. Math.61 (1995).

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Authors and Affiliations

  1. Department of Mathematics, Wuhan University, 430072, Wuhan, Hebei, P. R. C.

    Z. Chen, P. Fei & H. Zheng

Authors
  1. Z. Chen
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  2. P. Fei
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  3. H. Zheng
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Supported by NNSF of China and National 863 HTP.

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Chen, Z., Fei, P. & Zheng, H. A parallel quasi-Newton algorithm for unconstrained optimization. Computing 55, 125–133 (1995). https://doi.org/10.1007/BF02238097

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  • DOI: https://doi.org/10.1007/BF02238097

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