Applied Set-Valued Analysis and Optimization

Mircea Sofonea

Domingo A. Tarzia

Well-posedness and convergence results for elliptic hemivariational inequalities

椭圆型Hemivariational不等式的适定性与收敛性结果

In the recent time, the problem of finding common solutions of fixed point problems (FPPs) of nonlinear mappings and optimization problems (OPs) has received great research attention due to its potential applications to mathematical models whose constraints can be expressed as the FPPs and OPs.In this paper, we study the problem of finding a common solution of a split equilibrium problem (SEP), a variational inclusion problem (VIP) and the FPP with a finite family of multivalued demicontractive mappings.We propose a new inertial iterative method, which employs the forward-backward splitting technique together with the viscosity method for approximating the solution of the problem in Hilbert spaces.The proposed method uses variable step sizes, which do not depend on the norm of the bounded linear operator.We prove strong convergence results under some mild conditions.Finally, we present some numerical experiments to demonstrate the efficiency and applicability of the proposed method.Our result improves and extends several existing results in the current literature in this direction.

Victor Uzor

Timilehin Alakoya

Oluwatosin Mewomo

Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems

改进的前向后向分裂方法用于分裂平衡、变分包含和不动点问题

This paper is concerned with the problem of geodesic convex semi-infinite programming on Riemannian manifolds.First, we establish Karush-Kuhn-Tucker necessary optimality conditions for optimal solutions under the Guignard constraint qualification.Then, some characterizations of the solution sets of convex smooth semi-infinite programming on Riemannian manifolds are given.

L Tung

D Tam

V Singh

Characterization of solution sets of geodesic convex semi-infinite programming on Riemannian manifolds

黎曼流形上测地凸半无限规划解集的刻画

In this paper, we introduce a new self-adaptive inertial algorithm for finding a common solution of a split null point problem and a common fixed point problem of two infinite families of strict pseudo-contractive mappings and multivalued demicontractive mappings.We demonstrate a strong convergence result without a priori estimate of the norm of the linear operator in Hilbert spaces.As applications, we apply our main result to the split feasibility problem and the split minimization problem.Finally, we present a numerical example to show the efficient of the proposed algorithm.

Shufen Chen

Yaqin Wang

A self-adaptive inertial algorithm for solving split null point problems and common fixed point problems

求解分裂零点问题和公共不动点问题的自适应惯性算法

This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization.We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions.Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions.Finally, a Mond-Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined.

Huy Nguyen

Nguyen Hung

N Tuyen

Optimality conditions and duality relations in nonsmooth fractional interval-valued multiobjective optimization

非光滑分数区间值多目标优化中的最优性条件与对偶关系

We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems.Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom.The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online.This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees.These guarantees include linear convergence under a metric subregularity assumption.Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the Chambolle-Pock method and Krasnosel'skiȋ-Mann iterations.We propose a novel inertial primal-dual algorithm by selecting the deviations along a momentum direction and deciding their size by using the norm condition.Numerical experiments validate our convergence claims and demonstrate that even this simple choice of a deviation vector can enhance the performance compared to, for instance, the standard Chambolle-Pock algorithm.

Hamed Sadeghi

Sebastian Banert

Pontus Giselsson

Forward-backward splitting with deviations for monotone inclusions

带偏差的单调包含问题的前向后向分裂方法

. Hybrid stochastic differential equations (HSDEs) have wide range of real-world applications. In this paper, we study a new kind of nonlinear delayed neutral stochastic differential equations with Markovian switched noises (NHSDE-MSN). Under the assumption that this type of equations satisﬁes the locally Lipschitz condition and general condition of monotonicity, the existence and uniqueness of global solutions are established. Then, based on the Lyapunov function, M -matrix theory, stochastic analysis techniques, and Barbalat lemma, taking into account the delay as a bounded function, different decay stabilities of solutions are investigated. Finally, a numerical example is given to illustrate the utility of the main results.

Aziz Zouine

Chafai Imzegouan

Hassane Bouzahir

Cemil TUNC¸

Appl. Set-Valued Anal. Optim.

General decay stability of nonlinear delayed hybrid stochastic system with switched noises

非线性时滞混合随机系统在切换噪声下的总体衰减稳定性

In this paper, we obtain a generalization of a recent result of Tam (2018) which is for iterates of a set-valued paracontracting operators in a finite-dimensional space.Our result in this paper is obtained for operators in a metric space such that every its bounded and closed set is compact.We establish a convergence of inexact iterates of the set-valued operator by taking into account computational errors.

Alexander Zaslavski

Convergence of inexact iterates of an algorithm based on unions of nonexpansive mappings

基于非扩张映射并集的算法的不精确迭代的收敛性

In this paper, we study randomized and cyclic coordinate descent for convex unconstrained optimization problems.We improve the known convergence rates in some cases by using the numerical semidefinite programming performance estimation method.As a spin-off we provide a method to analyse the worst-case performance of the Gauss-Seidel iterative method for linear systems where the coefficient matrix is positive semidefinite with a positive diagonal.

Hadi Abbaszadehpeivasti

Etienne De Klerk

Moslem Zamani

Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming

凸优化中随机和循环坐标下降的收敛速度分析通过半定规划

ISSN	2562-7775, 2562-7783
h-index	10

Publication Information	Publisher: Biemdas Academic Publishers，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2019，Proportion of original research papers: ，Self Citation Rate:， Gold OA Rate:

Applied Set-Valued Analysis and Optimization

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Well-posedness and convergence results for elliptic hemivariational inequalities

Modified forward-backward splitting method for split equilibrium, variational inclusion, and fixed point problems

Characterization of solution sets of geodesic convex semi-infinite programming on Riemannian manifolds

A self-adaptive inertial algorithm for solving split null point problems and common fixed point problems

Optimality conditions and duality relations in nonsmooth fractional interval-valued multiobjective optimization

Well-posedness and convergence results for elliptic hemivariational inequalities

Forward-backward splitting with deviations for monotone inclusions

General decay stability of nonlinear delayed hybrid stochastic system with switched noises

Convergence of inexact iterates of an algorithm based on unions of nonexpansive mappings

Convergence rate analysis of randomized and cyclic coordinate descent for convex optimization through semidefinite programming