Page 617 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 617
ANALYSIS AND ITS APPLICATIONS
[3] F. A. BEREZIN, Covariant and contravariant symbols of operators, Math. USSR, Izv. 6
(1972) (1973), 1117–1151. (In English. Russian original.); translation from Russian Izv.
Akad. Nauk SSSR, Ser. Mat. 36 (1972), 1134–1167.
[4] M. HAJMOHAMADI, R. LASHKARIPOUR, M. BAKHERAD , Improve-
ments of Berezin number inequalities, Linear and Multilinear Algebra, doi:
10.1080/03081087.2018.1538310.
[5] M. BAKHERAD, U. YAMANCI, New estimations for the Berezin number inequality, J.
Inequal. Appl. 2020:40.
Numerical solution of Optimal Transport Problem on graphs
Enrico Facca, enrico.facca@sns.it
Scuola Normale Superiore Pisa, Italy
Coauthor: Michele Benzi
The Dynamical Monge-Kantorovich (DMK) model is dynamical system of equations whose
steady state has been related to the solution of the Optimal Transport Problem with cost equal
to the Euclidean distance. In this talk we present a re-adaption into a graph setting of the DMK
model, that can be rewritten in the form of a Gradient Flow. Using this formulation, we can
solve the OTP on graphs with cost given by the shortest path distance looking at the long-time
solution of the Gradient Flow equations. To this aim, we discretized the Gradient Flow equation
via backward Euler time-stepping, in order to use larger time steps, getting faster convergence
toward the optimal solution. The non-linear equations arising from such implicit time-stepping
scheme are solved via Newton-Raphson Method. Thus, the optimization problem is reduced to
the solution of a sequence of large and sparse saddle point linear systems, for which efficient
preconditioners have to be build. In this talk we present different preconditioning approaches
to tackle this problem.
On system of split generalised mixed equilibrium problem and fixed point
problems for multivalued mappings with no prior knowledge of operator
norm
Oluwatosin Temitope Mewomo, mewomoo@ukzn.ac.za
University of KwaZulu-Natal, Durban, South Africa
Coauthors: Timilehin Opeyemi Alakoya, Adeolu Taiwo
In this paper, we introduce system of split generalised mixed equilibrium problem, which is
more general than the existing well known split equilibrium problems and their generalisations,
split variational inequality problems and several other related problems. We propose a new it-
erative scheme with inertial term, which is independent on the operator norm and obtain strong
convergence result for approximating a common solution of the problem and fixed point of
finite family of multivalued demicontractive mappings. We obtain consequent results which
complement several existing results in this direction in the current literature. We also apply our
results to approximate the solution of split convex minimisation problems and present numeri-
cal examples to demonstrate the efficiency of our algorithm in comparison with some existing
615
[3] F. A. BEREZIN, Covariant and contravariant symbols of operators, Math. USSR, Izv. 6
(1972) (1973), 1117–1151. (In English. Russian original.); translation from Russian Izv.
Akad. Nauk SSSR, Ser. Mat. 36 (1972), 1134–1167.
[4] M. HAJMOHAMADI, R. LASHKARIPOUR, M. BAKHERAD , Improve-
ments of Berezin number inequalities, Linear and Multilinear Algebra, doi:
10.1080/03081087.2018.1538310.
[5] M. BAKHERAD, U. YAMANCI, New estimations for the Berezin number inequality, J.
Inequal. Appl. 2020:40.
Numerical solution of Optimal Transport Problem on graphs
Enrico Facca, enrico.facca@sns.it
Scuola Normale Superiore Pisa, Italy
Coauthor: Michele Benzi
The Dynamical Monge-Kantorovich (DMK) model is dynamical system of equations whose
steady state has been related to the solution of the Optimal Transport Problem with cost equal
to the Euclidean distance. In this talk we present a re-adaption into a graph setting of the DMK
model, that can be rewritten in the form of a Gradient Flow. Using this formulation, we can
solve the OTP on graphs with cost given by the shortest path distance looking at the long-time
solution of the Gradient Flow equations. To this aim, we discretized the Gradient Flow equation
via backward Euler time-stepping, in order to use larger time steps, getting faster convergence
toward the optimal solution. The non-linear equations arising from such implicit time-stepping
scheme are solved via Newton-Raphson Method. Thus, the optimization problem is reduced to
the solution of a sequence of large and sparse saddle point linear systems, for which efficient
preconditioners have to be build. In this talk we present different preconditioning approaches
to tackle this problem.
On system of split generalised mixed equilibrium problem and fixed point
problems for multivalued mappings with no prior knowledge of operator
norm
Oluwatosin Temitope Mewomo, mewomoo@ukzn.ac.za
University of KwaZulu-Natal, Durban, South Africa
Coauthors: Timilehin Opeyemi Alakoya, Adeolu Taiwo
In this paper, we introduce system of split generalised mixed equilibrium problem, which is
more general than the existing well known split equilibrium problems and their generalisations,
split variational inequality problems and several other related problems. We propose a new it-
erative scheme with inertial term, which is independent on the operator norm and obtain strong
convergence result for approximating a common solution of the problem and fixed point of
finite family of multivalued demicontractive mappings. We obtain consequent results which
complement several existing results in this direction in the current literature. We also apply our
results to approximate the solution of split convex minimisation problems and present numeri-
cal examples to demonstrate the efficiency of our algorithm in comparison with some existing
615
