We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for exampl...We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for example,the existence of solutions of the VIP and the monotonicity of the multivalued vector field,we prove that the sequence of the iterates given by the method converges to a solution of the problem.Furthermore,this convergence is linear or superlinear with respect to the Bregman distance.展开更多
Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applicat...Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.展开更多
文摘We present an extension of the proximal point method with Bregman distances to solve variational inequality problems(VIP)on Hadamard manifolds with null sectional curvature.Under some natural assumptions,as for example,the existence of solutions of the VIP and the monotonicity of the multivalued vector field,we prove that the sequence of the iterates given by the method converges to a solution of the problem.Furthermore,this convergence is linear or superlinear with respect to the Bregman distance.
文摘Monotonic regression （MR） is a least distance problem with monotonicity constraints induced by a partiaily ordered data set of observations. In our recent publication [In Ser. Nonconvex Optimization and Its Applications, Springer-Verlag, （2006） 83, pp. 25-33], the Pool-Adjazent-Violators algorithm （PAV） was generalized from completely to partially ordered data sets （posets）. The new algorithm, called CPAV, is characterized by the very low computational complexity, which is of second order in the number of observations. It treats the observations in a consecutive order, and it can follow any arbitrarily chosen topological order of the poset of observations. The CPAV algorithm produces a sufficiently accurate solution to the MR problem, but the accuracy depends on the chosen topological order. Here we prove that there exists a topological order for which the resulted CPAV solution is optimal. Furthermore, we present results of extensive numerical experiments, from which we draw conclusions about the most and the least preferable topological orders.
