Evolution of the 1984 KKM theorem of Ky Fan
, 2012 Recently we established the Knaster, Kuratowski, and Mazurkiewicz (KKM) theory on abstract convex spaces. In our research, we noticed that there are quite a few generalizations and applications of the 1984 KKM theorem of Ky Fan compared with his ...
Sehie Park
semanticscholar +1 more source
The convergence rate of a golden ratio algorithm for equilibrium problems [PDF]
arXiv, 2018 In this paper, we establish the $R$-linear rate of convergence of a golden ratio algorithm for solving an equilibrium problem in a Hilbert space. Several experiments are performed to show the numerical behavior of the algorithm and also to compare with others.
arxiv
Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme [PDF]
arXiv, 2019 A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers $TV$, $TGV^2$ and $NsTGV^2$. Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by $\Gamma$-convergence. Explicit examples and numerical
arxiv
Adaptive image processing: a bilevel structure learning approach for mixed-order total variation regularizers [PDF]
arXiv, 2019 A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous optimization with respect to parameters and the new class of regularizers, is studied.
arxiv
Determinants of pseudodifferential operators and complex deformations of phase space [PDF]
arXiv, 2001 Consider an h-pseudodifferential operator P, whose symbol extends holomorphically to a tubular neighborhood of the real phase space and converges sufficiently fast to 1, so that the determinant of P is well-defined. We show that the modulus of this determinant is asymptotically bounded by an exponential of the integral of the logarithm of the modulus ...
arxiv
New generalized systems of nonlinear ordered variational inclusions involving ⊕ operator in real ordered Hilbert spaces. [PDF]
J Inequal Appl, 2018 Sarfaraz M, Nisar KS, Morsy A, Ahmad MK.
europepmc +1 more source
Relaxed alternating CQ algorithms for the split equality problem in Hilbert spaces. [PDF]
J Inequal Appl, 2018 Yu H, Wang F.
europepmc +1 more source
An existence-uniqueness theorem and alternating contraction projection methods for inverse variational inequalities. [PDF]
J Inequal Appl, 2018 He S, Dong QL.
europepmc +1 more source
General iterative methods for systems of variational inequalities with the constraints of generalized mixed equilibria and fixed point problem of pseudocontractions. [PDF]
J Inequal Appl, 2018 Wang QW, Guan JL, Ceng LC, Hu B.
europepmc +1 more source
Multivalued backward stochastic differential equations with time delayed generators
Open Mathematics, 2014 Diomande Bakarime, Maticiuc Lucian
doaj +1 more source