Optimality conditions and duality for a class of nondifferentiable multiobjective generalized fractional programming problems

This paper studies a class of multiobjective generalized fractional programming problems, where the numerators of objective functions are the sum of differentiable function and convex function, while the denominators are the difference of differentiable function and convex function. Under the assumption of Calmness Constraint Qualification the Kuhn-Tucker type necessary conditions for efficient solution are given, and the Kuhn-Tucker type sufficient conditions for efficient solution are presented under the assumptions of （F, α, ρ, d）-V-convexity. Subsequently, the optimality conditions for two kinds of duality models are formulated and duality theorems are proved.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.

Nondifferentiable Multiobjective Programming under Generalized d_I-G-Type I Invexity

To relax convexity assumptions imposed on the functions in theorems on sufficient conditions and duality,new concepts of generalized d I-G-type I invexity were introduced for nondifferentiable multiobjective programming problems.Based upon these generalized invexity,G-Fritz-John(G-F-J)and G-KarushKuhn-Tucker(G-K-K-T)types sufficient optimality conditions were established for a feasible solution to be an efficient solution.Moreover,weak and strict duality results were derived for a GMond-Weir type dual under various types of generalized d I-G-type I invexity assumptions.

直流变换器广义对偶与相通性探讨

提出严格对偶和广义对偶的概念,探讨直流变换器的对偶性与相通性。对于三大类直流变换器,即Buck类、Boost类、Buck-Boost类变换器,包括隔离型和非隔离型,推导其严格对偶变换器,并分析可能存在的广义对偶变换器。对于一个已知的基本变换器,发现存在3个与其对偶的变换器,其中一个为严格对偶,两个为广义对偶。采用相通性,分析组合变换器与基本变换器之间的关联及在变换器推演上用到的相似处理方法,有利于变换器拓展与延伸。将软开关直流变换器看作是直流变换器与软开关电路的组合,可采用对偶与相通的方法对其进行研究。重点研究准谐振变换器的广义对偶与严格对偶,简要分析其余软开关直流变换器的对偶性。最后,通过分析直流变换器和软开关直流变换器仿真波形上的对偶性,验证理论分析的正确性。

国家治理视角下的总体性社会情绪

总体性社会情绪主要是指弥散在不同社会群体之中、容易形成共鸣并分享的一种相对一致的群体表达,是人们在社会认知、社会认同以及行为取向基础上形成的一种相对稳定的信念、精神和价值观。总体性社会情绪主要由社会认知、社会认同与行为取向组成,并通过满意度、社会信任与社会信心实现操作化,其功能则主要在于社会整合与结构维持。总体性社会情绪嵌入社会的结构之中,其结构的二重性表现为在总体性社会情绪引导下的社会行为既维持结构,又改变结构;对人们的行为有制约作用,同时也是行为的前提与条件。国家治理的过程实质上就是对这种总体性社会情绪的建构、解构和重构。通过总体性社会情绪来认识时代与社会,并将其作为国家治理政策工具的努力,具有重要的学术研究和政策启示价值。

Sufficiency and Duality for Nonsmooth Interval-Valued Optimization Problems via Generalized Invex-Infine Functions

In this paper,a new concept of generalized-affineness type of functions is introduced.This class of functions is more general than some of the corresponding ones discussed in Chuong(Nonlinear Anal Theory Methods Appl 75:5044–5052,2018),Sach et al.(J Global Optim 27:51–81,2003)and Nobakhtian(Comput Math Appl 51:1385–1394,2006).These concepts are used to discuss the sufficient optimality conditions for the interval-valued programming problem in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz functions.Furthermore,two types of dual problems,namely Mond–Weir type and mixed type duals are formulated for an interval-valued programming problem and usual duality theorems are derived.Our results improve and generalize the results appeared in Kummari and Ahmad(UPB Sci Bull Ser A 82(1):45–54,2020).

A TRUST REGION ALGORITHM VIA BILEVEL LINEAR PROGRAMMING FOR SOLVING THE GENERAL MULTICOMMODITY MINIMAL COST FLOW PROBLEMS

This paper proposes a nonmonotonic backtracking trust region algorithm via bilevel linear programming for solving the general multicommodity minimal cost flow problems.Using the duality theory of the linear programming and convex theory,the generalized directional derivative of the general multicommodity minimal cost flow problems is derived.The global convergence and superlinear convergence rate of the proposed algorithm are established under some mild conditions.

Duality for a Control Problem Involving Support Functions

Mond-Weir type duality for control problem with support functions is investigated under generalized convexity conditions. Special cases are derived. A relationship between our results and those of nonlinear programming problem containing support functions is outlined.

Efficiency and Duality in Nondifferentiable Multiobjective Programming Involving Directional Derivative

In this paper, we introduce a new class of generalized dI-univexity in which each component of the objective and constraint functions is directionally differentiable in its own direction di for a nondifferentiable multiobjective programming problem. Based upon these generalized functions, sufficient optimality conditions are established for a feasible point to be efficient and properly efficient under the generalised dI-univexity requirements. Moreover, weak, strong and strict converse duality theorems are also derived for Mond-Weir type dual programs.

从光电效应、波粒二象性到阿秒脉冲——2023年诺贝尔物理学奖

2023年诺贝尔物理学奖被授予皮埃尔•阿戈斯蒂尼、费伦茨•克劳斯和安妮•吕利耶,以表彰他们在阿秒脉冲的实验实现上作出的先驱性贡献。从电磁波的概念孕育之初到光电效应的揭示,再到激光与高次谐波的发现,人类渐渐揭示了光与物质交织舞蹈的深层复杂性。阿秒脉冲技术如同一把精致的钥匙,解锁了之前无法触及的物理世界的极短时间尺度的奥秘。如今,阿秒脉冲技术已广泛应用于能源、信息科技、医学等领域的研究,为我们提供了一种强大的探测手段。随着技术的不断发展和完善,我们有理由相信,在不远的将来它将在基础科学的探索和工业的革新中,产生更多意想不到的突破和飞跃。

教学智能化的数据权力滥用:表现、归因与纾解之策

教学智能化是当代教学发展的主旋律,旨在通过人工智能技术支撑与促进教学的变革,最终实现“因材施教”。但是,在智能化发展过程中,呈现出数据权力滥用的倾向。研究立足于生成论教学哲学的理论立场,结合吉登斯社会结构化理论对人类社会实践的分析思路,分析教学智能化数据权力滥用的原因,并提出相应的解决策略。教学智能化发展过程中的数据权力滥用具体表现为对人的主体数字化形象的塑造、对精准教学的推崇以及教学评价中“数据主义”倾向。究其原因,是社会群体的应试教育需求、教师等行动者自身实践意识的缺乏以及社会监管体系的不完备等多重原因相互作用产生的“复合效应”。对教学智能化发展中数据权力滥用的规制与消解可以从国家制度建设、社会观念革新与教师自我行为约束等方面入手,规制教师教育权力,规范教师教学行为。

存零约束优化问题的对偶问题

本文研究了近年提出的一类新优化问题存零约束优化问题,因存零约束的存在,使得求解最优解较困难.因此,本文针对存零约束优化问题,利用对偶理论提出了问题的Wolfe型对偶模型.在凸性和严格凸性假设下,获得了Wolfe对偶的弱、强、逆、限制逆和严格逆对偶结果.并进行了实例论证.

Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions

A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized （η,ρ）-invexity assumptions for a semi-infinite minmax fractional programming problem.

Morita Duality for the Rings of Generalized Power Series

Let A,B be associative rings with identity,and(S.≤)a strictly totally ordered monoid which is also artinian and finitely generated.For any bimodule AaMB. we show that the bimodule [[A^(S.≤)]][M^(S.≤)][[B^(S.≤)]]defines a Morita duality if and only if _AM_B defines a Morita duality and A is left noetherian.B is right noetherian.As a corollary,it.is shown that the ring[[A^(S.≤)]]of generalized power series over A has a Morita duality if and only if A is a left noetherian ring with a Morita duality induced by a bimodule _AM_B such that B is right noetherian.

Optimality Conditions and Duality for Nondifferentiable Multiobjective Semi-Infinite Programming Problems with Generalized(C,α,ρ,d)-Convexity

This paper obtains sufficient optimality conditions for a nonlinear nondifferentiable multiobjective semi-infinite programming problem involving generalized(C,α,ρ,d)-convex functions.The authors formulate Mond-Weir-type dual model for the nonlinear nondifferentiable multiobjective semiinfinite programming problem and establish weak,strong and strict converse duality theorems relating the primal and the dual problems.

计及可再生能源消纳的电热综合能源系统多目标优化模型

可再生能源因其清洁低碳的特点备受能源行业关注,在能源转型背景下,可再生能源受到关注和重视,已经成为能源转型的核心。可再生能源具有高效、清洁、低碳、环保等特点,发展可再生能源有利于促进生态环境和社会经济可持续发展。所以,我国能源发展的核心和关键环节是加快发展可再生能源。但是,可再生能源的不确定性也带来了严重的消纳问题。提高电力系统的灵活性去解决可再生能源的消纳问题成为当下研究热点之一。本文突破异质能源间的壁垒,基于电热综合能源系统去探索提高可再生能源的消纳能力。同时,立足于经济性与安全性指标,提出一种多目标优化数学模型,并通过对偶转化和行列生成算法对所提模型进行求解。最后,在算例测试中,通过对比电热综合能源系统与电力系统的各种测试指标证明了所提模型的有效性。

HIGHER-ORDER DUALITY FOR A CLASS OF NONDIFFERENTIABLE MULTIOBJECTIVE PROGRAMMING PROBLEMS INVOLVING GENERALIZED TYPE I AND RELATED FUNCTIONS

这份报纸扩大概括类型的班我工作由 Aghezzaf 和 Hachimi (2000 ) 介绍给高顺序的大小写的上下文并且提出很多高顺序的 duals 到一个非可辨的多客观的编程问题并且在高顺序的概括类型下面建立高顺序的两重性结果我在现在的纸介绍的功能。在文学反复出现的一种特殊情况是支持功能是一种积极半明确的二次的形式的方形的根。这和另外的特殊情况能乐意地从这些结果被产生。

Parametric Duality Models for Semiinfinite Multiobjective Fractional Programming Problems Containing Generalized (α, η, ρ)-V-Invex Functions

In this paper, we present several parametric duality results under various generalized （a,v,p）-V- invexity assumptions for a semiinfinite multiobjective fractional programming problem.