14 research outputs found
Inverse Problems for Nonlinear Quasi-Variational Inequalities with an Application to Implicit Obstacle Problems of -Laplacian Type
The primary objective of this research is to investigate an inverse problem
of parameter identification in nonlinear mixed quasi-variational inequalities
posed in a Banach space setting. By using a fixed point theorem, we explore
properties of the solution set of the considered quasi-variational inequality.
We develop a general regularization framework to give an existence result for
the inverse problem. Finally, we apply the abstract framework to a concrete
inverse problem of identifying the material parameter in an implicit obstacle
problem given by an operator of -Laplacian type
Existence of solutions for implicit obstacle problems of fractional laplacian type involving set-valued operators
The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis
Monotone Inclusions, Acceleration and Closed-Loop Control
We propose and analyze a new dynamical system with a closed-loop control law
in a Hilbert space , aiming to shed light on the acceleration
phenomenon for \textit{monotone inclusion} problems, which unifies a broad
class of optimization, saddle point and variational inequality (VI) problems
under a single framework. Given
that is maximal monotone, we propose a closed-loop control system that is
governed by the operator , where a feedback law
is tuned by the resolution of the algebraic equation
for some
. Our first contribution is to prove the existence and uniqueness
of a global solution via the Cauchy-Lipschitz theorem. We present a simple
Lyapunov function for establishing the weak convergence of trajectories via the
Opial lemma and strong convergence results under additional conditions. We then
prove a global ergodic convergence rate of in terms of a gap
function and a global pointwise convergence rate of in terms of a
residue function. Local linear convergence is established in terms of a
distance function under an error bound condition. Further, we provide an
algorithmic framework based on the implicit discretization of our system in a
Euclidean setting, generalizing the large-step HPE framework. Although the
discrete-time analysis is a simplification and generalization of existing
analyses for a bounded domain, it is largely motivated by the above
continuous-time analysis, illustrating the fundamental role that the
closed-loop control plays in acceleration in monotone inclusion. A highlight of
our analysis is a new result concerning -order tensor algorithms for
monotone inclusion problems, complementing the recent analysis for saddle point
and VI problems.Comment: Accepted by Mathematics of Operations Research; 42 Page
15th Conference on Dynamical Systems Theory and Applications DSTA 2019 ABSTRACTS
From Preface: This is the fifteen time when the conference „Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to
participate in the conference for the first time. With proud and satisfaction we welcome nearly 255 persons from 47 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 338 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference edited books.Technical editor and cover design: Kaźmierczak, MarekCover design: Ogińska, Ewelina; Kaźmierczak, Mare