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(F,α,ρ,d)-凸性下一类多目标分式规划问题的最优性条件和对偶

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四川大学学报（自然科学版） 2009年第6期46卷 1623-1627页

作者：吴泽忠 Ze-Zhong 成都信息工程学院计算科学系成都610041

作者在(F,α,ρ,d)-凸性条件下讨论了一类多目标分式规划问题的最优性条件和对偶.通过将多目标分式规划问题转化为多目标规划问题,作者建立了原问题的最优性充分条件并获得了弱对偶和强对偶结果.

关键词：凸性条件多目标分式规划问题最优性条件弱对偶 class optimality condition optimality duality theorem 最优性充分条件原问题强对偶讨论结果

Detecting Arrays and Their optimality

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Acta Mathematica Sinica,English Series 2011年第12期27卷 2309-2318页

作者： Yu TANG Jian Xing YIN Department of Mathematics Soochow University Suzhou 215006 P. R. China

Detecting arrays were proposed by Colbourn and McClary in 2008, which are of interest in generating software test suites to cover all t-sets of component interactions and detect interaction faults in component-based systems. So far, optimality and constructions of detecting arrays have not been studied systematically. Indeed, no useful benchmark to measure the optimality of detecting arrays has previously been given, and only some sporadic examples of optimal detecting arrays have been found. This paper tries to take the first step by presenting a lower bound on the size of detecting arrays and some methods of constructing optimal detecting arrays. A number of infinite series of optimal detecting arrays are then obtained.

关键词： Detecting arrays interaction faults bounds optimality constructions

optimality for Multi-Objective Programming Involving Arcwise Connected d-Type-I Functions

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American Journal of Operations Research 2011年第4期1卷 243-248页

作者： Guolin Yu Min Wang Research Institute of Information and System Computation Science The North University for Ethnics

This paper deals with the optimality conditions and dual theory of multi-objective programming problems involving generalized convexity. New classes of generalized type-I functions are introduced for arcwise connected functions, and examples are given to show the existence of these functions. By utilizing the new concepts, several sufficient optimality conditions and Mond-Weir type duality results are proposed for non-differentiable multi-objective programming problem.

关键词： Multi-Objective Programming Pareto Efficient Solution Arcwise Connected d-Type-I Functions optimality Conditions Duality

Higher-order optimality Conditions and Duality for Approximate Solutions in Non-convex Set-valued Optimization

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 620-628页

作者： Guo-lin YU Tian-tian GONG North Minzu University

This paper deals with higher-order optimality conditions and duality theory for approximate solutions in vector optimization involving non-convex set-valued maps.Firstly,under the assumption of near cone-subconvexlikeness for set-valued maps,the higher necessary and sufficient optimality conditions in terms of Studniarski derivatives are derived for local weak approximate minimizers of a set-valued optimization problem.Then,applications to Mond-Weir type dual problem are presented.

关键词： studniarski derivatives optimality conditions set-valued optimization problem efficiency duality

An Adaptive hp-DG-FE Method for Elliptic Problems: Convergence and optimality in the 1D Case

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Communications on Applied Mathematics and Computation 2019年第3期1卷 309-331页

作者： Paola Antonietti Claudio Canuto Marco Verani MOX-Dipartimento di Matematica Politecnico di MilanoP.zza Leonardo Da Vinci 3220133 MilanItaly Dipartimento di Scienze Matematiche Politecnico di TorinoCorso Duca degli Abruzzi 2410129 TurinItaly

We propose and analyze an hp-adaptive DG-FEM algorithm, termed hp-ADFEM, and its one-dimensional realization, which is convergent, instance optimal, and h- and p-robust. The procedure consists of iterating two routines:one hinges on Binev's algorithm for the adaptive hp-approximation of a given function, and finds a near-best hp-approximation of the current discrete solution and data to a desired accuracy;the other one improves the discrete solution to a finer but comparable accuracy, by iteratively applying D?rfler marking and h refinement.

关键词： Elliptic problem Discontinuous Galerkin method hp-adaptivity Convergence and optimality

optimality conditions for a class of distributed parameter system

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Chinese Science Bulletin 1996年第18期41卷 1501-1505页

作者：高夯 Institute of Mathematics Fudan University Shanghai 200433 China

the (?) satisfying (4) is called an optimal control, and the corresponding state (?)(x)=y(x;(?)) is called an optimal state and ((?),(?)) is referred to as an optimal pair In ref. [1], Casas considers the system governed by linear elliptic equation, which involves control in coefficient, and the phase space of control is convex and the cost functional is convex. Casas obtained the necessary conditions of optimal control by using convex analysis theories. In this note, the phase space of control is not convex and the cost func-

关键词： elliptic equation distributed parameter system optimality condition.

Solution Concepts and New optimality Conditions in Bilevel Multiobjective Programming

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Applied Mathematics 2012年第10期3卷 1395-1402页

作者： Francisque Fouodji Dedzo Laure Pauline Fotso Calice Olivier Pieume Department of Computer Sciences Faculty of Science University of Yaoundé I Yaoundé Cameroon Department of Mathematics Faculty of Science University of Yaoundé I Yaoundé Cameroon Regional Bureau for Education in Africa Pole de Dakar UNESCO Dakar Senegal

In this paper, new sufficient optimality theorems for a solution of a differentiable bilevel multiobjective optimization problem (BMOP) are established. We start with a discussion on solution concepts in bilevel multiobjective programming;a theorem giving necessary and sufficient conditions for a decision vector to be called a solution of the BMOP and a proposition giving the relations between four types of solutions of a BMOP are presented and proved. Then, under the pseudoconvexity assumptions on the upper and lower level objective functions and the quasiconvexity assumptions on the constraints functions, we establish and prove two new sufficient optimality theorems for a solution of a general BMOP with coupled upper level constraints. Two corollary of these theorems, in the case where the upper and lower level objectives and constraints functions are convex are presented.

关键词： Bilevel Multiobjective Optimization Multiobjective Optimization Sufficient optimality Condition Strict Convexity Pseudoconvexity Quasiconvexity

基于Pareto optimality的PPP项目三大主参与方效用探讨

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沈阳建筑大学学报（社会科学版） 2011年第4期13卷 418-421页

作者：陈黎明赵辉青岛理工大学管理学院山东青岛266520

在PPP项目的众多参与方中,选取项目发起人、SPC和贷款银行三个最主要的参与方,通过分析项目发起人与SPC、SPC与贷款银行和贷款银行与项目发起人之间的内在联系,在Pareto optimality理论分析的基础上,得到三者之间两两优势互补的埃奇沃... 详细信息

在PPP项目的众多参与方中,选取项目发起人、SPC和贷款银行三个最主要的参与方,通过分析项目发起人与SPC、SPC与贷款银行和贷款银行与项目发起人之间的内在联系,在Pareto optimality理论分析的基础上,得到三者之间两两优势互补的埃奇沃思方框图,并根据瓦尔拉斯均衡理论得出PPP项目能够实现帕累托最优,实现项目效用的最大化,最后拟画出PPP项目三大主参与方的效用可能性曲线。

关键词： PPP Pareto optimality 埃奇沃思效用

English-Chinese Phonemic Equivalents Constraints in Transliteration from the Perspective of optimality Theory

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海外英语 2014年第12X期 262-263页

作者：肖瑞珠 Foreign Languages Dept.JiShou University

Transliteration aims to adapt loanwords to perfect sound patterns and structures. With the guidance of optimality Theory, this paper elaborates on the constraints that must be observed in transliteration to achieve Chinese phonological harmony from phonemic equivalents. It analyzes the ranking of constraints for structural acceptability of the loanwords.

关键词： transliteration optimality Theory phonemic equival