In this paper, we consider minimization problems with constraints. We show that, if the set of constraints is a Finslerian manifold of non-positive flag curvature, and the objective function is differentiable and satisfies the Kurdyka-Lojasiewicz property, then the proximal point method can be natur...

Perspectives in eye-tracking technology for applications in education

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Raimundo da Silva Soares Jr et al. (1 janv. 2023)

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BACKGROUND: Many students struggle with mathematics difficulties, such as arithmetic problem-solving, intuitive geometry concepts and learning disabilities. Currently, there is an increasingly interesting in applying neuroscientific research paradigms to elucidate mathematical thinking and neural me...

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

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Glaydston de Carvalho Bento et al.

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In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we...

Generalized Proximal Distances for Bilevel Equilibrium Problems

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G. Bento et al.

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We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distances. We propose a framework for the convergence analysis of the sequence generated by the algorithm. This class of probl...

Learning how to Play Nash, Potential Games and Alternating Minimization Method for Structured Nonconvex Problems on Riemannian Manifolds

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Joao Xavier Cruz Neto et al. (2013)

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We consider minimization problems with constraints. We show that if the set of constraints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfies the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space...