Residual Selection in A Projection Method for Convex Minimization Problems

We propose a new method of subgradient selection in a projection method with level control for convex minimization problems. The presented selection ensures long steps and leads to an essential acceleration of the convergence of projection methods.

[1]  S. Agmon The Relaxation Method for Linear Inequalities , 1954, Canadian Journal of Mathematics.

[2]  A. Conn,et al.  An Efficient Method to Solve the Minimax Problem Directly , 1978 .

[3]  Philip E. Gill,et al.  Numerical Linear Algebra and Optimization , 1991 .

[4]  Sehun Kim,et al.  Variable target value subgradient method , 1991, Math. Program..

[5]  Jochem Zowe,et al.  A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results , 1992, SIAM J. Optim..

[6]  Andrzej Cegielski,et al.  Projection onto an acute cone and convex feasibility problem , 1993, System Modelling and Optimization.

[7]  Yurii Nesterov,et al.  New variants of bundle methods , 1995, Math. Program..

[8]  K. Kiwiel The Efficiency of Subgradient Projection Methods for Convex Optimization , 1996 .

[9]  K. Kiwiel The efficiency of subgradient projection methods for convex optimization, part I: general level methods , 1996 .

[10]  K. Kiwiel Monotone gram matrices and deepest surrogate inequalities in accelerated relaxation methods for convex feasibility problems , 1997 .

[11]  Andrzej Cegielski,et al.  A method of projection onto an acute cone with level control in convex minimization , 1999, Math. Program..

[12]  Robert Dylewski,et al.  Numerical behavior of the method of projection onto an acute cone with level control in convex minimization , 2000 .

[13]  A. Cegielski Obtuse cones and Gram matrices with nonnegative inverse , 2001 .

[14]  Andrzej Cegielski,et al.  Selection strategies in projection methods for convex minimization problems , 2002 .