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On Poljak's improved subgradient method

  • S. Kim
  • S. Koh
Technical Note

Abstract

Poljak has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a more acute angle with the direction toward the set of optimal solutions than that in the subgradient method.

Key Words

Optimization nondifferentiable optimization subgradient methods cutting plane methods 

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References

  1. 1.
    Ermoliev, Yu. N.,Methods for Solving Nonlinear Extremal Problems, Cybernetics, No. 4, pp. 1–17, 1966.Google Scholar
  2. 2.
    Poljak, B. T.,Minimization of Unsmooth Functionals, USSR Computational Mathematics and Mathematical Physics, Vol. 9, pp. 14–29, 1969.Google Scholar
  3. 3.
    Lemarechal, C.,Nonsmooth Optimization and Descent Methods, International Institute for Applied Systems Analysis, Laxenburg, Austria, Report No. RR-78-04, 1978.Google Scholar
  4. 4.
    Kiwiel, K. C.,An Aggregate Subgradient Method for Nonsmooth Convex Minimization, Mathematical Programming, Vol. 27, pp. 320–341, 1983.Google Scholar
  5. 5.
    Bazaraa, M. S., andGoode, J. J.,A Least-Distance Programming Procedure for Minimization Problems under Linear Constraints, Journal of Optimization Theory and Applications, Vol. 40, pp. 489–514, 1983.Google Scholar
  6. 6.
    Lemke, C. E.,On Complementary Pivot Theory, Mathematics of the Decision Sciences, Edited by G. R. Dantzig and A. F. Veinott, American Mathematical Society, Providence, Rhode Island, 1968.Google Scholar
  7. 7.
    Wolfe, P.,Finding the Nearest Point in a Polytope, Mathematical Programming, Vol. 11, pp. 128–149, 1976.Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • S. Kim
    • 1
  • S. Koh
    • 1
  1. 1.Department of Management ScienceKorea Advanced Institute of Science and TechnologySeoulKorea

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