Fixed Point Theory and Algorithms for Sciences and Engineering
ESCI-ISI
2730-5422
Cơ quản chủ quản: N/A
Phân tích ảnh hưởng
Các bài báo tiêu biểu
An adaptive splitting algorithm for the sum of two generalized monotone operators and one cocoercive operator
Tập 2021 Số 1 - 2021
AbstractSplitting algorithms for finding a zero of sum of operators often
involve multiple steps which are referred to as forward or backward steps.
Forward steps are the explicit use of the operators and backward steps involve
the operators implicitly via their resolvents. In this paper, we study an
adaptive splitting algorithm for finding a zero of the sum of three operators.
We assume that two ...
On the nonlinear Hadamard-type integro-differential equation
Tập 2021 Số 1 - 2021
AbstractThis paper studies uniqueness of solutions for a nonlinear Hadamard-type
integro-differential equation in the Banach space of absolutely continuous
functions based on Babenko’s approach and Banach’s contraction principle. We
also include two illustrative examples to demonstrate the use of main theorems.
Well-posedness analysis of a stationary Navier–Stokes hemivariational inequality
- 2021
AbstractThis paper provides a well-posedness analysis for a hemivariational
inequality of the stationary Navier-Stokes equations by arguments of convex
minimization and the Banach fixed point. The hemivariational inequality
describes a stationary incompressible fluid flow subject to a nonslip boundary
condition and a Clarke subdifferential relation between the total pressure and
the normal compone...
String-averaging methods for best approximation to common fixed point sets of operators: the finite and infinite cases
- 2021
AbstractString-averaging is an algorithmic structure used when handling a family
of operators in situations where the algorithm in hand requires to employ the
operators in a specific order. Sequential orderings are well known, and a
simultaneous order means that all operators are used simultaneously (in
parallel). String-averaging allows to use strings of indices, constructed by
subsets of the ind...
Convergence of proximal splitting algorithms in $\operatorname{CAT}(\kappa)$ spaces and beyond
- 2021
AbstractIn the setting of$\operatorname{CAT}(\kappa)$CAT(κ)spaces, common fixed
point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky–Mann
relaxations, nonlinear projected-gradients) converge locally linearly under the
assumption of linear metric subregularity. Linear metric subregularity is in any
case necessary for linearly convergent fixed point sequences, so the result is
tig...
History-dependent operators and prox-regular sweeping processes
- 2022
AbstractWe consider an abstract inclusion in a real Hilbert space, governed by
an almost history-dependent operator and a time-dependent multimapping with
prox-regular values. We establish the unique solvability of the inclusion under
appropriate assumptions on the data. The proof is based on the arguments of
monotonicity, fixed point, and prox-regularity. We then use our result in order
to deduce...
Thuật toán ngưỡng thu nhỏ lặp cải tiến nhanh với sai số cho bài toán phục hồi hình ảnh Dịch bởi AI
- 2021
Tóm tắtTrong bài báo này, chúng tôi giới thiệu một phương pháp phân tách
tiến-lùi lặp mới với sai số để giải quyết vấn đề bao gồm biến phân của tổng hai
toán tử đơn điệu trong không gian Hilbert thực. Chúng tôi đề xuất và phân tích
phương pháp này dưới một số điều kiện nhẹ nhàng thích hợp áp dụng cho các tham
số, sao cho một định lý hội tụ mạnh khác cho những vấn đề này được thiết lập.
Chúng tôi c...
Stochastic approximation method using diagonal positive-definite matrices for convex optimization with fixed point constraints
- 2021
AbstractThis paper proposes a stochastic approximation method for solving a
convex stochastic optimization problem over the fixed point set of a
quasinonexpansive mapping. The proposed method is based on the existing adaptive
learning rate optimization algorithms that use certain diagonal
positive-definite matrices for training deep neural networks. This paper
includes convergence analyses and con...
Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces
Tập 2022 Số 1 - 2022
AbstractLet E be a strictly convex real Banach space and let $D\subseteq E$ D ⊆
E be a nonempty closed convex subset of E. Let $T_{i}: {D}\longrightarrow
\mathcal{P}({D})$ T i : D ⟶ P ( D ) , $i=1,2,3,\ldots $ i = 1 , 2 , 3 , … be a
countable family of quasinonexpansive multivalued maps that are continuous with
respect to the Hausdorff metric, $\mathcal{P}(D)$ P ( D ) is the family of
proximinal a...
Existence of solutions for a Lipschitzian vibroimpact problem with time-dependent constraints
- 2022
AbstractWe study a mechanical system with a finite number of degrees of freedom,
subjected to perfect time-dependent frictionless unilateral (possibly nonconvex)
constraints with inelastic collisions on active constraints. The dynamic is
described in the form of a second-order measure differential inclusion. Under
some regularity assumptions on the data, we establish several properties of the
set ...