Geodesic
Numerical behavior of the method of projection onto an acute cone with level control in convex minimization
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 2, pp. 147-158.

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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 
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Dylewski, Robert. Numerical behavior of the method of projection onto an acute cone with level control in convex minimization. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 20 (2000) no. 2, pp. 147-158. http://geodesic.mathdoc.fr/item/DMDICO_2000_20_2_a0/

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