Interior quasi-subgradient method with non-Euclidean distances for constrained quasi-convex optimization problems in hilbert spaces

An interior quasi-subgradient method is proposed based on the proximal distance to solve constrained nondifferentiable quasi-convex optimization problems in Hilbert spaces. It is shown that a newly introduced generalized Gâteaux subdifferential is a subset of a quasi-subdifferential. The convergence properties, including the global convergence and iteration complexity, are investigated under the assumption of the Hölder condition of order p,...