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1.
This paper introduces a concept of differentiability for functions in several variables which has a very natural definition and shares all the properties one expects of a notion of differentiability, but is shown to be weaker than the usual concept of differentiability defined as local linearizability. The exact connection between the two different concepts is exhibited.  相似文献   

2.
In this paper, we study some concepts of generalized differentials for set-valued maps and introduce some new ones. In particular we first focus on the concept of Generalized Differential Quotients, briefly GDQs. It is shown that minimal GDQs are unique for scalar single-valued functions, then GDQs are compared with contingent and Dini derivatives, finally some other results characterizing GDQs are given. A new definition of generalized differentiation theory is presented, namely weak GDQs that are a modification of GDQs. We clarify the relationships with other concepts of generalized differentiability: Clarke generalized Jacobians, path-integral generalized differentials and Warga derivate containers. Finally, some applications of GDQs end the paper.   相似文献   

3.
通过所提出的模糊数值函数的强可导性和平均 Mc Shane可积性等概念 ,对模糊数值函数的连续性从导数和积分两方面进行了讨论和刻画 ,也回答了强可导性与强导数可积之间的关系 ,给出两个充分必要条件。  相似文献   

4.
Norde et al. [Games Econ. Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent. A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull [Econ. Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.  相似文献   

5.
根据实际均衡问题研究的需要,给出了模糊向量、模糊值函数、模糊矩阵等新概念,建立了模糊均衡问题的数学模型,即模糊线性互补问题。在引入新的模糊期望的基础上,研究了其性质,并据此给出了模糊线性互补问题的一种确定型等价式及此类问题的均衡解的概念。用实例说明了所提模型和方法的合理性及应用前景。  相似文献   

6.
In this paper, we interpret a two-point boundary value problem for a second order fuzzy differential equation by using a generalized differentiability concept. We present a new concept of solutions and, utilizing the generalized differentiability, we investigate the problem of finding new solutions. Some examples are provided for which the new solutions are found.  相似文献   

7.
In this article, we revisit the concept of strong differentiability of real functions of one variable, underlying the concept of differentiability. Our discussion is guided by the Straddle Lemma, which plays a key role in this context. The proofs of the results presented are designed to meet a young audience in mathematics, typical of students in a first course of Real Analysis or an honors-level Calculus course.  相似文献   

8.
9.
《Optimization》2012,61(4):497-513
This paper deals with necessary conditions for optimization problems with infinitely many inequality constraints assuming various differentiability conditions. By introducing a second topology N on a topological vector space we define generalized versions of differentiability and tangential cones. Different choices of N lead to Gâteaux-, Hadamaed- and weak differentiability with corresponding tangential cones. The general concept is used to derive necessary conditions for local optimal points in form of inequalities and generalized multiplier rules, Special versions of these theorems are obtained for different differentiability assumptions by choosing properly. An application to approximation theory is given.  相似文献   

10.
This paper deals with the approximation of nonlinear initial-value problems by difference methiods. in the Present part I The basic definitions and concepts are presented and equivalence theorems for stability and continuous convergenc are proved. Here, The differentiability condition (d) and the boundedness condition (Bp) are of fundamental siginificance. the latter is one of the equivalent characterizations of stability. The equivalence theorems for stability and continuous convergence include characterizations by means of locally uniform two-sided Lipschitz conditions and tow-sided discertization error estimates. At the end of part I a generalized of the concept of stable convergence of Dahlquist [2] and Torng [16] is proved to series of equivalent conditions convergence. in part II the above results will yields a series of equivalent conditions for the concepts of weak stability and conditions convergence of certain order. Moreover, further convergence concepts for semi-homogeneous methods will be studied, and hyperbolic and parawbolic example will be treated  相似文献   

11.
A new solution concept for two-player zero-sum matrix games with multi-dimensional payoffs is introduced. It is based on extensions of the vector order in \(\mathbb {R}^d\) to order relations in the power set of \(\mathbb {R}^d\), so-called set relations, and strictly motivated by the interpretation of the payoff as multi-dimensional loss for one and gain for the other player. The new concept provides coherent worst case estimates for games with multi-dimensional payoffs. It is shown that–in contrast to games with one-dimensional payoffs–the corresponding strategies are different from equilibrium strategies for games with multi-dimensional payoffs. The two concepts are combined into new equilibrium notions for which existence theorems are given. Relationships of the new concepts to existing ones such as Shapley and vector equilibria, vector minimax and maximin solutions as well as Pareto optimal security strategies are clarified.  相似文献   

12.
This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability.  相似文献   

13.
优化和均衡的等价性   总被引:2,自引:0,他引:2  
陈光亚 《系统科学与数学》2009,29(11):1441-1446
通过向量优化问题, 向量变分不等式问题以及向量变分原理来分析优化问题及均衡问题的一致性.从而显然, 可以用统一的观点来处理数值优化、向量优化以及博弈论等问题.进而为非线性分析提供了一个新的发展空间.  相似文献   

14.
We find some estimates for the derivatives of equilibrium states of subshifts of finite type. We prove the differentiability (with respect to the potential) of integrals of certain discontinuous functions for the equilibrium state of a potential.research supported by CNPq, Brazil  相似文献   

15.
In this paper we establish links between desirable properties satisfied by familiar solutions to bargaining games with a variable population and the Nash equilibrium concept for threat bargaining games. We introduce three new concepts for equilibrium threat strategies called strategic stability, strategic monotonicity with respect to changes in the number of agents and strategic constancy. Our primary objective in this paper is to show that familiar assumptions satisfied by bargaining games with a variable population yield equilibrium threat strategies which satisfies in a very natural way the concepts we have introduced.  相似文献   

16.
《Optimization》2012,61(2):365-388
Abstract

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a numerical approach which basically ignores the possible nondifferentiabilities.  相似文献   

17.
Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.  相似文献   

18.
The concepts of differentiability, convexity, generalized convexity and minimization of a fuzzy mapping are known in the literature. The purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using Buckley–Feuring approach for fuzzy differentiation and derive Karush–Kuhn–Tucker condition for the constrained fuzzy minimization problem.  相似文献   

19.
We introduce and discuss measure of non-Radon–Nikodym property to investigate differentiability of continuous convex functions on Banach spaces. Using this new concept, we establish some results about Asplund spaces and generic Fréchet differentiability of continuous convex functions on non-Asplund spaces.Mathematics Subject Classifications (2000) 46B22, 49J50, 49J53.  相似文献   

20.
Sensitivity analysis for nonsmooth generalized equations   总被引:3,自引:0,他引:3  
Results pertaining to Lipschitzian and directional differentiability properties for solutions to generalized equations under very general perturbations are obtained with the aid of new differentiation concepts for multivalued maps.Research supported in part by grants from the Air Force Office of Scientific Research and the National Science Foundation.  相似文献   

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