On Auxiliary Principle for Equilibrium Problems
By Giandomenico Mastroeni. 2003
264 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/a73e3769a296cbc603dc5162cc09c040222033e0
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In Applied Mathematics
In Computational Theory and Mathematics
In Numerical Analysis
Citations in the corpus
- Parallel Extragradient-Proximal Methods for Split Equilibrium Problems (2015, methodology): “Hypothesis (A2) was introduced by Mastroeni [23] to prove the convergence of the auxiliary principle method for solving an equilibrium problem.”
- On extragradient-viscosity methods for solving equilibrium and fixed point problems in a Hilbert space (2015, background): “On the other hand, condition (A5) is a Lipschitztype condition introduced by Mastroeni [4] to prove the convergence of the Auxiliary Principle Method for solving an equilibrium problem.”
- Explicit iterative algorithms for solving equilibrium problems (2019, background): “A bifunction f : C × C → satisfies a Lipschitz-type condition [23] if there exist two constants c1, c2 > 0 such that f (x, y) + f (y, z) ≥ f (x, z) − c1||x − y||2 − c2||y − z||2, ∀x, y ∈ C .”
- Existence of equilibria via Ekeland's principle (2005, methodology): “Along this line, Cohen [7] developed s methods for solving VI and optimization problems, and Mastroeni [10] generalized focusing the attention on fixed-point formulations of (EP).”
- Extragradient algorithms extended to equilibrium problems (2008, methodology): “We omit the proof for this nondifferentiable case because it is similar to the one given in [17,23] for differentiable case.”
- New extragradient method for a class of equilibrium problems in Hilbert spaces (2018, methodology): “Mastroeni [8] further extended the auxiliary problem principle to equilibrium problems involving strongly monotone bifunctions.”