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Variable Target Subgradient Method of Projection onto an Acute Cone in Convex Minimization

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Part of the book series: Operations Research Proceedings ((ORP,volume 1995))

Abstract

In this paper, we consider the convex minimization problem

$$ \min imize\,f(x)\,subject\,to\,x \in D $$
(1)

where f: IRn → IR is a convex function and D ⊂ IRn is a convex, closed and bounded subset. We suppose that \( M: = Arg{\min_{{x \in D}}}f(x) \ne \phi \), i.e. f attains its minimum on D.

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References

  1. Cegielski, A., On a relaxation algorithm in convex optimization problems, Technical Report, Institute of Mathematics, Higher College of Engineering, Zielona Góra, Poland, 1992.

    Google Scholar 

  2. Cegielski, A., Relaxation Methods in Convex Optimization Problems, Higher College of Engineering, Series Monographies, No. 67, Zielona Góra, Poland 1993 (Polish).

    Google Scholar 

  3. Cegielski, A., Projection onto an acute cone and convex feasibility problems, in Lecture Notes in Control and Information Science 197, J. Henry and J.-P. Yvon, eds., Springer-Verlag, London, 1994, pp. 187–194.

    Google Scholar 

  4. Kim, S., Ahn, H., Cho, S.-C., Variable target value subgradient method, Mathematical Programming 49 (1991) 359–369.

    Article  Google Scholar 

  5. Kiwiel, K. C., Block-iterative surrogate projection methods for convex feasibility problems, Linear Algebra and Applications, (1994) (to appear).

    Google Scholar 

  6. Kiwiel, K. C., The efficiency of subgradient projection methods for convex optimization, part I: General level methods, Technical Report, System Research Institute, Warsaw 1994.

    Google Scholar 

  7. Kiwiel, K. C., The efficiency of subgradient projection methods for convex optimization, part II: Implementations and extensions, Technical Report, System Research Institute, Warsaw 1994.

    Google Scholar 

  8. C. Lemaréchal, A. S. Nemirovskii and YU. E. Nesterov, New variants of bundle methods, Research Report 1508, INRIA, Roquencourt, 1991.

    Google Scholar 

  9. Polyak, B. T., Minimization of unsmooth functionals, Zh. Vychisl. Mat. i Mat. Fiz. 9 (1969) 509–521 (Russian). English translation in U.S.S.R. Comput. Math. and Math. Phys. 9 (1969) 14–29.

    Google Scholar 

  10. Shchepakin, M. B., On a modification of a class of algorithms for mathematical programming, Zh. Vychisl. Mat. i Mat. Fiz. 19 (1979) 1387–1395 (Russian).

    Google Scholar 

  11. Todd, M. J., Some remarks on the relaxation method for linear inequalities, Technical Report 419, Cornell University, Cornell, Ithaca, 1979.

    Google Scholar 

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© 1996 Springer-Verlag Berlin Heidelberg

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Cegielski, A. (1996). Variable Target Subgradient Method of Projection onto an Acute Cone in Convex Minimization. In: Kleinschmidt, P., Bachem, A., Derigs, U., Fischer, D., Leopold-Wildburger, U., Möhring, R. (eds) Operations Research Proceedings 1995. Operations Research Proceedings, vol 1995. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80117-4_4

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  • DOI: https://doi.org/10.1007/978-3-642-80117-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60806-6

  • Online ISBN: 978-3-642-80117-4

  • eBook Packages: Springer Book Archive

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