A Proximal Point Algorithm with Bregman Distances for Quasiconvex Optimization over the Positive Orthant
نویسندگان
چکیده
We present an interior proximal point method with Bregman distance, whose Bregman function is separable and the zone is the interior of the positive orthant, for solving the quasiconvex optimization problem under nonnegative constraints. We establish that the sequence generated by our algorithm is well defined and we prove convergence to a solution point when the sequence of parameters goes to zero. When the parameters are bounded above, we get the convergence to a KKT point.
منابع مشابه
An Extension of the Proximal Point Method for Quasiconvex Minimization
In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex objective functions on the Euclidean space and the nonnegative orthant. For the unconstrained minimization problem, assumming that the function is bounded from below and lower semicontinuous we prove that iterations {x} given by 0 ∈ ∂̂(f(.)+(λk/2)||.−x||)(x) are well defined and if,...
متن کاملProximal Point Methods for Quasiconvex and Convex Functions With Bregman Distances on Hadamard Manifolds
This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on noncompact Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to a class of quasi...
متن کاملProximal Point Method for a Class of Bregman Distances on Riemannian Manifolds
This paper generalizes the proximal point method using a class of Bregman distances to solve convex and quasiconvex optimization problems on complete Riemannian manifolds. We will prove, under standard assumptions, that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we give some examples of Bregman distances in non-Euclidean spaces.
متن کاملProximal Point Methods for Functions Involving Lojasiewicz, Quasiconvex and Convex Properties on Hadamard Manifolds
This paper extends the full convergence of the proximal point method with Riemannian, Semi-Bregman and Bregman distances to solve minimization problems on Hadamard manifolds. For the unconstrained problem, under the assumptions that the optimal set is nonempty and the objective function is continuous and either quasiconvex or satisfies a generalized Lojasiewicz property, we prove the full conve...
متن کاملOn Dual Convergence of the Generalized Proximal Point Method with Bregman Distances
TTie use of generalized distances (e.g.. Bregman distances), instead of Ihe Euclidean one, in the proximal point method for convex optimization, allows for elimination of the inequality constraints from the subproblems. In this paper we consider the proximal point method with Bregman distances applied to linearly constrained convex optimization problems, and study the behavior of the dual seque...
متن کامل