4 papers
Subgradient Methods on Manifolds with Lower Bounded Curvature
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +1
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting poi…
Busemann-coupling subdifferentials and Fenchel biconjugation on Hadamard manifolds
G. C. Bento, J. X. Cruz Neto, I. D. L. Melo
We introduce an intrinsic subdifferential on Hadamard manifolds induced by a base-point-dependent Busemann coupling, motivated by the scarcity of nonconstant affine functions on no…
A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +2
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Paret…
Elements of Convex Geometry in Hadamard Manifolds with Application to Equilibrium Problems
G. C. Bento, J. X. Cruz Neto, I. D. L. Melo
In this paper, is introduced a new proposal of resolvent for equilibrium problems in terms of the Busemann's function. A great advantage of this new proposal is that, in addition t…