Extensions of subgradient projection algorithms (Q1089262)

Let \(\Omega\) be a nonempty, open, convex subset of \({\mathbb{R}}^ n\) and \(f,g_ i,v_ j:\Omega\to {\mathbb{R}}\), \(i=1,...,m\); \(j=1,...,r\); be convex, differentiable functions. In this paper the problem of minimizing \(f(x)+v(x)\) is considered, subject to \(g_ i(x)\leq 0\), \(i=1,...,m\), where \(v(x)=\max \{v_ j(x):\) \(j=1,...,r\}\). A subgradient projection algorithm is proposed. This algorithm is a slight modification of the algorithms previously published by the author [ibid. 35, 111-126 (1982; Zbl 0486.65042); ibid. 41, 217-243 (1984; Zbl 0546.65040)]. It is designed to handle the situation where the function f(x) is not necessarily strictly convex. An appropriate modification of the corresponding proofs of convergence is given.