ArticleOriginal scientific text

Title

Numerical behavior of the method of projection onto an acute cone with level control in convex minimization

Authors 1

Affiliations

  1. Institute of Mathematics, Technical University, ul. Podgórna 50, PL-65-246 Zielona Góra, Poland

Abstract

We present the numerical behavior of a projection method for convex minimization problems which was studied by Cegielski [1]. The method is a modification of the Polyak subgradient projection method [6] and of variable target value subgradient method of Kim, Ahn and Cho [2]. In each iteration of the method an obtuse cone is constructed. The obtuse cone is generated by a linearly independent system of subgradients. The next approximation of a solution is the projection onto a translated acute cone which is dual to the constructed obtuse cone. The target value which estimates the minimal objective value is updated in each iteration. The numerical tests for some tests problems are presented in which the method of Cegielski [1] is compared with the method of Kim, Ahn and Cho [2].

Keywords

convex nondifferentiable minimization, projection method, subgradient method, acute cone, obtuse cone

Bibliography

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  2. S. Kim, H. Ahn and S.-C. Cho, Variable target value subgradient method, Mathematical Programming 49 (1991), 359-369.
  3. K.C. Kiwiel, Methods of Descent for Nondifferentiable Optimization, Springer-Verlag, Berlin 1985.
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  6. B.T. Polyak, Minimization of unsmooth functionals, Zh. Vychisl. Mat. i Mat. Fiz. 9 (1969), 509-521 (Russian).
  7. H. Schramm and J. Zowe, A version of the bundle idea for minimizing a nonsmooth function: conceptual idea, convergence analysis, numerical results, SIAM J. Optimization 2 (1992), 121-152.
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Pages:
147-158
Main language of publication
English
Received
1999-11-05
Accepted
2000-03-07
Published
2000
Exact and natural sciences