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1.
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems. This paper is dedicated to Professor Franco Giannessi for his 68th birthday  相似文献
2.
A circular membrane with an arbitrarily placed internal strip of small length is concerned in this article. A two-term asymptotic expansion for the fundamental frequency of the membrane, as the length of the strip approaching to zero, is specified. Comparing it with the one [8] derived for the membrane with an internal circular core, it is found that the position of the internal constraint has more effect than the shape of the internal constraint on the fundamental frequency. The asymptotic approximation is also compared with the numerical data computed by the dual boundary element method [2] for a circular membrane of radius 1 with a radially placed internal strip of length 2c. These two sets of data are in good agreement. The relative error is less than 3 % as c is less than or equal to 0.1, for all positions of the strip. Moreover, the relative error is less than 1 % as c is less than or equal to 0.01.  相似文献
3.
In this paper, we introduce a new class of vector quasi-equilibrium problems with set-valued maps. Almost all the vector equilibrium models of the Blum-Oettli type in the literature are special cases of our new class of equilibrium problems under consideration. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the -diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for such vector equilibrium problems.  相似文献
4.
In this paper, an algorithm for constrained minimax problems is presented which is globally convergent and whose rate of convergence is two-step superlinear. The algorithm applies SQP to the constrained minimax problems by combining a nonmonotone line search and a second-order correction technique, which guarantees a full steplength while close to a solution, such that the Maratos effect is avoided and two-step superlinear convergence is achieved.  相似文献
5.
In this paper we discuss the problem of estimating the common mean of a bivariate normal population based on paired data as well as data on one of the marginals. Two double sampling schemes with the second stage sampling being either a simple random sampling (SRS) or a ranked set sampling (RSS) are considered. Two common mean estimators are proposed. It is found that under normality, the proposed RSS common mean estimator is always superior to the proposed SRS common mean estimator and other existing estimators such as the RSS regression estimator proposed by Yu and Lam (1997, Biometrics, 53, 1070–1080). The problem of estimating the mean Reid Vapor Pressure (RVP) of regular gasoline based on field and laboratory data is considered.  相似文献
6.
We consider the problems of dientifying the parametersa ij (x), b i (x), c(x) in a 2nd order, linear, uniformly elliptic equation, $$\begin{gathered} - \partial _i (a_{ij} (x)\partial _j u) + b_i (x)\partial _i u + c(x)u = f(x),in\Omega , \hfill \\ \partial _v u|_{\partial \Omega } = \phi (s),s \in \partial \Omega , \hfill \\ \end{gathered}$$ on the basis of measurement data $$u(s) = z(s),s \in B \subset \partial \Omega ,$$ with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gâteaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters.  相似文献
7.
A circular membrane with an arbitrarily placed internal strip of small length is concerned in this article. A two-term asymptotic expansion for the fundamental frequency of the membrane, as the length of the strip approaching to zero, is specified. Comparing it with the one [8] derived for the membrane with an internal circular core, it is found that the position of the internal constraint has more effect than the shape of the internal constraint on the fundamental frequency. The asymptotic approximation is also compared with the numerical data computed by the dual boundary element method [2] for a circular membrane of radius 1 with a radially placed internal strip of length 2c. These two sets of data are in good agreement. The relative error is less than 3 % as c is less than or equal to 0.1, for all positions of the strip. Moreover, the relative error is less than 1 % as c is less than or equal to 0.01.  相似文献
8.
We introduce in the present paper a Gauss–Newton-type method for solving generalized equations defined by sums of differentiable mappings and set-valued mappings in Banach spaces. Semi-local convergence and local convergence of the Gauss–Newton-type method are analyzed.  相似文献
9.
In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncertain payoff parameters, but only knows that they belong to an uncertainty set. In our model, the players use a robust optimization approach for each of their objective to contend with payoff uncertainty. To formulate such a game, named “robust multiple objective games” here, we introduce three kinds of robust equilibrium under different preference structures. Then, by using a scalarization method and an existing result on the solutions for the generalized quasi-vector equilibrium problems, we obtain the existence of these robust equilibria. Finally, we give an example to illustrate our model and the existence theorems. Our results are new and fill the gap in the game theory literature.  相似文献
10.
Ranking data appear in everyday life and arise in many fields of study such as marketing, psychology and politics. Very often, the key objective of analyzing and modeling ranking data is to identify underlying factors that affect the individuals’ choice behavior. Factor analysis for ranking data is one of the most widely used methods to tackle the aforementioned problem. Recently, Yu et al. [J R Stat Soc Ser A (Statistics in Society) 168:583–597, 2005] have developed factor models for ranked data in which each individual is asked to rank a set of items. However, paired ranked data may arise when the same set of items are ranked by a pair of judges such as a couple in a family. This paper extended the factor model to accommodate such paired ranked data. The Monte Carlo expectation-maximization algorithm was used for parameter estimation, at which the E-step is implemented via the Gibbs Sampler. For model assessment and selection, a tailor-made method called the bootstrap predictive checks approach was proposed. Simulation studies were conducted to illustrate the proposed estimation and model selection method. The proposed method was applied to analyze a parent–child partially ranked data collected from a value priorities survey carried out in the United States.  相似文献