PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2002 | 22 | 1 | 97-123
Tytuł artykułu

Selection strategies in projection methods for convex minimization problems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We propose new projection method for nonsmooth convex minimization problems. We present some method of subgradient selection, which is based on the so called residual selection model and is a generalization of the so called obtuse cone model. We also present numerical results for some test problems and compare these results with some other convex nonsmooth minimization methods. The numerical results show that the presented selection strategies ensure long steps and lead to an essential acceleration of the convergence of projection methods.
Twórcy
  • Institute of Mathematics, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
  • Institute of Mathematics, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
Bibliografia
  • [1] A. Cegielski, Projection onto an acute cone and convex feasibility problems, J. Henry and J.-P. Yvon (eds.), Lecture Notes in Control and Information Science 197, Springer- Verlag, London (1994), 187-194.
  • [2] A. Cegielski, A method of projection onto an acute cone with level control in convex minimization, Mathematical Programming 85 (1999), 469-490.
  • [3] A. Cegielski, Obtuse cones and Gram matrices with non-negative inverse, Linear Algebra and its Applications 335 (2001), 167-181.
  • [4] A. Cegielski and R. Dylewski, Residual selection in a projection method for convex minimization problems, (submitted).
  • [5] J. Charalambous and A.R. Conn, An efficient method to solve the minimax problem directly, SIAM J. Num. Anal. 15 (1978), 162-187.
  • [6] R. Dylewski, Numerical behavior of the method of projection onto an acute cone with level control in convex minimization, Discuss. Math. Differential Inclusions, Control and Optimization 20 (2000), 147-158.
  • [7] S. Kim, H. Ahn and S.-C. Cho, Variable target value subgradient method, Mathematical Programming 49 (1991), 359-369.
  • [8] K.C. Kiwiel, The efficiency of subgradient projection methods for convex optimization, part I: General level methods, SIAM J. Control and Optimization 34 (1996), 660-676.
  • [9] K.C. Kiwiel, The efficiency of subgradient projection methods for convex optimization, part II: Implementations and extensions, SIAM J. Control and Optimization 34 (1996), 677-697.
  • [10] K.C. Kiwiel, Monotone Gram matrices and deepest surrogate inequalities in accelerated relaxation methods for convex feasibility problems, Linear Algebra and Applications 252 (1997), 27-33.
  • [11] C. Lemaréchal and R. Mifflin, A set of nonsmooth optimization test problems, Nonsmooth Optimization, C. Lemarechal, R. Mifflin, (eds.), Pergamon Press, Oxford 1978, 151-165.
  • [12] C. Lemaréchal, A.S. Nemirovskii and Yu.E. Nesterov, New variants of bundle methods, Math. Progr. 69 (1995), 111-147.
  • [13] N.Z. Shor, Minimization Methods for Non-differentiable Functions, Springer-Verlag, Berlin 1985.
  • [14] H. Schramm and J. Zowe, A version of the bundle idea for minimizing of a nonsmooth function: conceptual idea, convergence analysis, numerical results, SIAM J. Control and Optimization 2 (1992), 121-152.
  • [15] M.J. Todd, Some remarks on the relaxation method for linear inequalities,. Technical Report 419 (1979), Cornell University.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1034
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.