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math.OC2026
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…
math.OC2024
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…
math.OC2021
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…