Differential Inclusions, Control and Optimization 20 (2000) 147-158
doi: 10.7151/dmdico.1009

## NUMERICAL BEHAVIOR OF THE METHOD OF PROJECTION ONTO AN ACUTE CONE WITH LEVEL CONTROL IN CONVEX MINIMIZATION

Robert Dylewski

Institute of Mathematics, Technical University
ul. Podgórna 50, PL-65-246 Zielona Góra, Poland

e-mail: r.dylewski@im.uz.zgora.pl

## Abstract

We present the numerical behavior of a projection method for convex minimization problems which was studied by Cegielski [1]. The method is a modification of the Polyak subgradient projection method [6] and of variable target value subgradient method of Kim, Ahn and Cho [2]. In each iteration of the method an obtuse cone is constructed. The obtuse cone is generated by a linearly independent system of subgradients. The next approximation of a solution is the projection onto a translated acute cone which is dual to the constructed obtuse cone. The target value which estimates the minimal objective value is updated in each iteration. The numerical tests for some tests problems are presented in which the method of Cegielski [1] is compared with the method of Kim, Ahn and Cho [2].

Keywords: convex nondifferentiable minimization, projection method, subgradient method, acute cone, obtuse cone.

1991 Mathematics Subject Classification: 65K05, 90C25.

## References

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