The Concave Nontransitive Consumer

The preference of a concave nontransitive consumer is represented by a skew-symmetric and concave-convex bifunction on the set of all commodity bundles. This paper characterizes finite sets of demand observations that are consistent with the demand behavior of such kind of consumer by a generalized monotonicity property.     

广义均值保持变换的随机单调性及其在库存系统中的应用

本文提出一类非线性且均值可能不等的广义均值保持变换,研究实现其变换前后随机变量比较的充分条件或充分必要条件,并用此变换来定量刻画需求不确定性对库存系统决策和利润的影响。首先给出变换前后或不同参数下分布函数的关系及其满足一阶随机占优和割准则序的充分条件,特征刻画此变换与广义TTT变换之间的关系。进一步,用三类特殊的广义均值保持变换进行验证。最后,将此变换应用到报童模型中,得出该变换对包含最小化成本及最大化利润的一致化报童问题的随机单调性。     

Generalized Invexity and Generalized Invariant Monotonicity

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.     

Seven kinds of monotone maps

Known as well as new types of monotone and generalized monotone maps are considered. For gradient maps, these generalized monotonicity properties can be related to generalized convexity properties of the underlying function. In this way, pure first-order characterizations of various types of generalized convex functions are obtained.     

Functional ANOVA,ultramodularity and monotonicity: Applications in multiattribute utility theory

Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker’s preference structure. These properties are usually characterized via partial derivatives. However, elicitation methods do not necessarily lead to twice-differentiable utility functions. Furthermore, while in a single-attribute context concavity fully reflects risk aversion, in multiattribute problems such correspondence is not one-to-one. We show that Tsetlin and Winkler’s multivariate risk attitudes imply ultramodularity of the utility function. We demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA). The necessary and sufficient conditions under which monotonicity and/or ultramodularity of single-attribute functions imply the monotonicity and/or ultramodularity of the corresponding multiattribute function under additive, preferential and mutual utility independence are then established without reliance on the utility function differentiability. We also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision-maker’s multivariate risk attitudes.     

Merit functions and error bounds for constrained mixed set-valued variational inequalities via generalized f-projection operators

In this paper, we introduce and investigate a constrained mixed set-valued variational inequality (MSVI) in Hilbert spaces. We prove the solution set of the constrained MSVI is a singleton under strict monotonicity. We also propose four merit functions for the constrained MSVI, that is, the natural residual, gap function, regularized gap function and D-gap function. We further use these functions to obtain error bounds, i.e. upper estimates for the distance to solutions of the constrained MSVI under strong monotonicity and Lipschitz continuity. The approach exploited in this paper is based on the generalized f-projection operator due to Wu and Huang, but not the well-known proximal mapping.     

MONOTONICITY AND INEQUALITIES FOR THE GENERALIZED DISTORTION FUNCTION

The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηg（a,t）, and obtain some inequalities for ηk（a, t） and relative distortion functions.     

Some inequalities for the generalized linear distortion function

In this paper,we establish several inequalities for the the generalized linear distortion function λ(a,K) by using the monotonicity and convexity of certain combinations λ(a,K).     

Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems

In this paper, we consider the existence and multiplicity of solutions of second-order Hamiltonian systems. We propose a generalized asymptotically linear condition on the gradient of Hamiltonian function, classify the linear Hamiltonian systems, prove the monotonicity of the index function, and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear Hamiltonian systems by global analysis methods such as the Leray-Schauder degree theory, the Morse theory, the Ljusternik-Schnirelman theory, etc.     

Generalized monotonicity and convexity of non-differentiable functions

The relationships between (strict, strong) convexity of non-differentiable functions and (strict, strong) monotonicity of set-valued mappings, and (strict, strong, sharp) pseudo convexity of non-differentiable functions and (strict, strong) pseudo monotonicity of set-valued mappings, as well as quasi convexity of non-differentiable functions and quasi monotonicity of set-valued mappings are studied in this paper. In addition, the relations between generalized convexity of non-differentiable functions and generalized co-coerciveness of set-valued mappings are also analyzed.     

供应提前期和需求不确定下库存系统的随机比较

本文研究供应提前期和需求不确定下包含最小化成本和最大化利润的一致化报童问题中随机比较实现的充分条件,并通过随机比较定量刻画提前期和需求不确定性对库存系统决策和利润的影响。首先引入报童收益函数,给出其优化前后满足随机占优及拉普拉斯变换序的充分条件。进一步,在周期需求服从指数分布的情形下,定量刻画固定提前期与提前期服从几何分布两种情况的随机单调性。最后,将上述结论应用到报童模型中,得到提前期需求对一致化报童问题的随机单调性。     

广义Taylor中值函数若干分析性质

文[2-8]对微分中值定理及Taylor定理"中间点"的渐近性质进行了研究,本文在此基础上,给出了"广义Taylor中值函数"的定义,对"广义Taylor中值函数"的分析性质进行了系统的讨论,证明了"广义Taylor中值函数"的单调性、可积性、连续性、可微性等分析性质.     

Generalized Monotone Operators on Dense Sets

In the present work we show that the local generalized monotonicity of a lower semicontinuous set-valued operator on some certain type of dense sets ensures the global generalized monotonicity of that operator. We achieve this goal gradually by showing at first that the lower semicontinuous set-valued functions of one real variable, which are locally generalized monotone on a dense subsets of their domain are globally generalized monotone. Then, these results are extended to the case of set-valued operators on arbitrary Banach spaces. We close this work with a section on the global generalized convexity of a real valued function, which is obtained out of its local counterpart on some dense sets.     

Generalized Invariant Monotonicity and Invexity of Non-differentiable Functions

This paper is devoted to the study of relationships between several kinds of generalized invexity of locally Lipschitz functions and generalized monotonicity of corresponding Clarke’s subdifferentials. In particular, some necessary and sufficient conditions of being a locally Lipschitz function invex, quasiinvex or pseudoinvex are given in terms of momotonicity, quasimonotonicity and pseudomonotonicity of its Clarke’s subdifferential, respectively. As an application of our results, the existence of the solutions of the variational-like inequality problems as well as the mathematical programming problems (MP) is given. Our results extend and unify the well known earlier works of many authors.     

On optimal bidding and inventory control in sequential procurement auctions: the multi period case

We consider the problem of a firm that in each cycle of a planning horizon builds inventory of identical items that it acquires by participating in auctions in order to satisfy its own market demand. The firm’s objective is to have a procurement strategy that maximizes the expected present value of the profit for an infinite planning horizon of identical cycles. We formulate this problem as a Markov decision process. We establish monotonicity properties of the value function and of the optimal bidding rule.     

Coercivity Conditions for Equilibrium Problems

The study of the existence of solutions of equilibrium problems on unbounded domains involves usually the same sufficient assumptions as for bounded domains together with a coercivity condition. We focus on two different conditions: the first is obtained assuming the existence of a bounded set such that no elements outside is a candidate for a solution; the second allows the solution set to be unbounded. Our results exploit the generalized monotonicity properties of the function f defining the equilibrium problem. It turns out that, in both the pseudomonotone and the quasimonotone setting, an equivalence can be stated between the nonemptyness and boundedness of the solution set and these coercivity conditions. In the pseudomonotone case, we compare our coercivity conditions with various coercivity conditions that appeared in the literature.We thank an anonymous referee for valuable comments and suggestions.     

Generalized Convexity of Functions and Generalized Monotonicity of Set-Valued Maps

We establish connections between some concepts of generalized monotonicity for set-valued maps introduced earlier and some notions of generalized convexity. Moreover, a notion of pseudomonotonicity for set-valued maps is introduced; it is shown that, if a function f is continuous, then its pseudoconvexity is equivalent to the pseudomonotonicity of its generalized subdifferential in the sense of Clarke and Rockafellar.     

关于伽玛函数的单调性质

伽玛函数的单调性质和对数完全单调性质被获得了.     

On the structural properties of a discrete-time single product revenue management problem

We consider a multi-period revenue management problem in which multiple classes of demand arrive over time for the common inventory. The demand classes are differentiated by their revenues and their arrival distributions. We investigate monotonicity properties of varying problem parameters on the optimal reward and the policy.     

Characterizations of relatively generalized monotone maps

New concepts of relative monotonicity were introduced in Konnov (Oper Res Lett 28:21–26, 2001a) which extend the usual ones. These concepts enable us to establish new existence and uniqueness results for variational inequality problems over product sets. This paper presents first-order characterizations of new (generalized) monotonicity concepts. Specialized results are obtained for the affine case.