Invited Session Mon.1.H 2051

Monday, 10:30 - 12:00 h, Room: H 2051

Cluster 24: Variational analysis [...]

Equilibrium problems and related topics


Chair: Alfredo Noel Iusem



Monday, 10:30 - 10:55 h, Room: H 2051, Talk 1

Orizon Pereira Ferreira
Local convergence of Newton's method under majorant condition in Riemannian manifolds

Coauthor: Roberto C M Silva


A local convergence analysis of Newton's method for finding a singularity of a differentiable vector field defined on a complete Riemannian manifold, based on majorant principle, is presented in this paper. This analysis provides a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the vector field under consideration. It also allows us to obtain the optimal convergence radius, the biggest range for the uniqueness of the solution, and to unify some previous unrelated results.



Monday, 11:00 - 11:25 h, Room: H 2051, Talk 2

Susana Scheimberg
A reflection-projection method for equilibrium problems

Coauthor: Paulo Santos


We consider an implementable algorithm for solving nonsmooth equilibrium problems in finite-dimensional spaces. The algorithm combines the strategy of generating a feasible point, by using reflections related to hyperplanes, and the
projected-type subgradient method where the projection is done onto a suitable half-space. The algorithm has a low computational cost per iteration. Computational experience is reported and comparative analysis with other algorithms is also given.



Monday, 11:30 - 11:55 h, Room: H 2051, Talk 3

Luis Mauricio GraƱa Drummond
New strategies for vector optimization problems

Coauthor: E. H. Fukuda


Under partial orders derived from arbitrary closed convex pointed cones with nonempty interior, we propose extensions of scalar optimization procedures to the vector setting. For constrained vector-valued optimization, we seek efficient/weakly efficient points by adapting classical real-valued strategies. Assuming reasonable hypotheses, we establish some convergence results to optimal points.


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