Projection method with level control in convex minimization

• Autorzy: Robert Dylewski
• Języki publikacji: EN

Abstrakty

EN

We study a projection method with level control for nonsmoooth convex minimization problems. We introduce a changeable level parameter to level control. The level estimates the minimal value of the objective function and is updated in each iteration. We analyse the convergence and estimate the efficiency of this method.

Słowa kluczowe

EN

projection method; convex nondifferentiable minimization; level control

Kategorie tematyczne

• 65K05: Mathematical programming methods
• 90C25: Convex programming

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 1
• Strony: 101-120

Daty

wydano

2010

otrzymano

2009-05-10

Twórcy

autor

Robert Dylewski

• Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516 Zielona Góra, ul. Prof. Z. Szafrana 4a, Poland

Bibliografia

• [1] A. Cegielski, Relaxation Methods in Convex Optimization Problems, Higher College of Engineering, Series Monographies, No. 67 (1993), Zielona Góra, Poland (Polish).
• [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 and R. Dylewski, Selection strategies in projection methods for convex minimization problems, Discuss. Math. Differential Inclusions, Control and Optimization 22 (2002), 97-123. doi:10.7151/dmdico.1034
• [4] A. Cegielski and R. Dylewski, Residual selection in a projection method for convex minimization problems, Optimization 52 (2003), 211-220.
• [5] S. Kim, H. Ahn and S.-C. Cho, Variable target value subgradient method, Mathematical Programming 49 (1991), 359-369.
• [6] 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.
• [7] C. Lemaréchal, A.S. Nemirovskii and Yu.E. Nesterov, New variants of bundle methods, Mathematical Programming 69 (1995), 111-147.
• [8] B.T. Polyak, Minimization of unsmooth functionals, Zh. Vychisl. Mat. i Mat. Fiz. 9 (1969), 509-521.

Identyfikatory

DOI

10.7151/dmdico.1114