A proximal point algorithm with a ϕ-divergence for quasiconvex programming
F.G.M. Cunha, J. X. Cruz Neto, Paulo Roberto Oliveira · Optimization · 2010
We apply the proximal point method with the ϕ-divergence given by for the minimization of quasiconvex functions subject to non-negativity constraints. We prove, without the assumption of the boundedness level to the objective function, that the sequence generated by our algorithm is well-defined and it converges to a stationary point when the regularization parameter λ k satisfies , for some . If, in addition, , we then obtain the convergence to an optimal solution. We verify the effectiveness of the proximal algorithm via numerical experiments accomplished with randomly generated test problems.