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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1114, author = {Robert Dylewski}, title = {Projection method with level control in convex minimization}, journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization}, volume = {30}, year = {2010}, pages = {101-120}, zbl = {1201.65099}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1114} }
Robert Dylewski. Projection method with level control in convex minimization. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 30 (2010) pp. 101-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1114/
[000] [1] A. Cegielski, Relaxation Methods in Convex Optimization Problems, Higher College of Engineering, Series Monographies, No. 67 (1993), Zielona Góra, Poland (Polish).
[001] [2] A. Cegielski, A method of projection onto an acute cone with level control in convex minimization, Mathematical Programming 85 (1999), 469-490. | Zbl 0973.90057
[002] [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 | Zbl 1175.90310
[003] [4] A. Cegielski and R. Dylewski, Residual selection in a projection method for convex minimization problems, Optimization 52 (2003), 211-220. | Zbl 1057.49021
[004] [5] S. Kim, H. Ahn and S.-C. Cho, Variable target value subgradient method, Mathematical Programming 49 (1991), 359-369. | Zbl 0825.90754
[005] [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. | Zbl 0846.90084
[006] [7] C. Lemaréchal, A.S. Nemirovskii and Yu.E. Nesterov, New variants of bundle methods, Mathematical Programming 69 (1995), 111-147. | Zbl 0857.90102
[007] [8] B.T. Polyak, Minimization of unsmooth functionals, Zh. Vychisl. Mat. i Mat. Fiz. 9 (1969), 509-521.