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

 

Abstract:
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

 

Abstract:
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

 

Abstract:
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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