Numerical behavior of the method of projection onto an acute cone with level control in convex minimization (Q2717929)

The author studies the convex minimization problem NEWLINE\[NEWLINE\text{minimize}\quad f(x)\quad\text{subject to }x\in D,\tag{1}NEWLINE\]NEWLINE where \(f:\mathbb{R}^n\to \mathbb{R}\) is a convex function (not necessarily differentiable), \(D\subset\mathbb{R}\) is a convex compact subset. He analyses the numerical behaviour of a projection method onto an acute cone with level control as applied to solving (1). The method can be considered as a modification of the Pólyak subgradient projection method and of variable target value subgradient method of \textit{S. Kim}, \textit{H. Ahn} and \textit{S.-C. Cho} [Math. Program. Ser. A 49, No. 3, 359-369 (1991; Zbl 0825.90754)]. More precisely, it is based on the projection onto a translated acute cone which is dual to the obtuse cone generated at each iteration by a linearly independent system of subgradients. The numerical comparison of the projection method under discussion with the method of Kim, Ahn and Cho [loc. cit.] is the main aim of the paper.