In this paper, a new nonlinear scalarization function, which is a generalization of the oriented distance function, is introduced. Some properties of the function are discussed. Then the function is applied to obtain ...
详细信息
In this paper, a new nonlinear scalarization function, which is a generalization of the oriented distance function, is introduced. Some properties of the function are discussed. Then the function is applied to obtain some new optimality conditions and scalar representations for set-valued vector optimization problems with set optimization criteria. In terms of the function and the image space analysis, some new alternative results for generalized parametric systems are derived.
In this paper, we study a scalarizationfunction and introduce well-posedness notions for set optimization problems. Some scalarization results are given for the sets of weak m-minimal solutions and m-minimal solution...
详细信息
In this paper, we study a scalarizationfunction and introduce well-posedness notions for set optimization problems. Some scalarization results are given for the sets of weak m-minimal solutions and m-minimal solutions for set optimization problems. Furthermore, we introduce novel concepts of well-posedness specifically tailored for the set optimization problem. We establish connections among three distinct types of well-posedness and explore the relationships that exist between the well-posedness of set optimization problems and that of scalar optimization problems.
In this paper, the lower and upper semicontinuity of the solution mappings for parametric unified weak vector equilibrium problem (PUWVEP) are established, via free-disposal set and non-linear scalarizationfunction. ...
详细信息
In this paper, the lower and upper semicontinuity of the solution mappings for parametric unified weak vector equilibrium problem (PUWVEP) are established, via free-disposal set and non-linear scalarizationfunction. Moreover, example is given to illustrate the obtained results. The results improve the corresponding ones in the literature [Z.Y. Peng and S.S. Chang, Optim. Lett. (2014) 8 159-169.], [Z.Y. Peng, X.B. Li, X.J. Long and X.D. Fan, Optim. Lett. (2018) 12 1339-1356.], [Z.Y. Peng, J.W. Peng, X.J. Long and J.C. Yao, J. Global Optim. 70 (2018) 55-69.].
This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are d...
详细信息
This paper focuses on the study of multistage stochastic vector generalized quasi-variational inequalities with a variable ordering structure. The proposed multistage stochastic vector quasi-variational problems are defined in a suitable functional setting relative to a finite set of final possible states and certain information fields;these formulations are a multicriteria extension of the multistage stochastic variational inequalities. A relevant aspect of these problems is the presence of the nonanticipativity constraints on the variables of the problem;stage by stage, these constraints impose the measurability with respect to the information field at that stage. Without requiring any assumption of monotonicity, we prove some existence results by using a nonlinearscalarization technique. On this basis, we analyze multistage stochastic vector Nash equilibrium problems: as an example, we focus on a suitable multistage stochastic bicriteria Cournot oligopolistic model.
In this paper, we consider strong vector equilibrium problems in normed spaces. Firstly, we study stability conditions for a scalar equilibrium problem without assuming boundedness and concavity properties of the cons...
详细信息
In this paper, we consider strong vector equilibrium problems in normed spaces. Firstly, we study stability conditions for a scalar equilibrium problem without assuming boundedness and concavity properties of the constraint map and objective function, respectively. Next, we discuss properties of the Hiriart-Urruty oriented distance function in an ordered space, and then using these properties, relationships between the strong equilibrium problems and the scalar ones are formulated. Then after, based on these relationships, we address sufficient conditions for the Lipschitz continuity of approximate solution maps to vector equilibrium problems via the corresponding results of the scalar equilibrium problems. As an application, we apply the obtained results to express stability conditions for network equilibrium problems.
The main results of the paper are a minimal element theorem and an Ekeland-type variational principle for set-valued maps whose values are compared by means of a weighted set order relation. This relation is a mixture...
详细信息
The main results of the paper are a minimal element theorem and an Ekeland-type variational principle for set-valued maps whose values are compared by means of a weighted set order relation. This relation is a mixture of a lower and an upper set relation which form the building block for modern approaches to set-valued optimization. The proofs rely on nonlinear scalarization functions which admit to apply the extended Brezis-Browder theorem. Moreover, Caristi's fixed point theorem and Takahashi's minimization theorem for set-valued maps based on the weighted set order relation are obtained and the equivalences among all these results is verified. An application to generalized intervals is given which leads to a clear interpretation of the weighted set order relation and versions of Ekeland's principle which might be useful in (computational) interval mathematics.
In this paper, we employ the image space analysis method to investigate a vector optimization problem with non-cone constraints. First, we use the linear and nonlinear separation techniques to establish Lagrange-type ...
详细信息
In this paper, we employ the image space analysis method to investigate a vector optimization problem with non-cone constraints. First, we use the linear and nonlinear separation techniques to establish Lagrange-type sufficient and necessary optimality conditions of the given problem under convexity assumptions and generalized Slater condition. Moreover, we give some characterizations of generalized Lagrange saddle points in image space without any convexity assumptions. Finally, we derive the vectorial penalization for the vector optimization problem with non-cone constraints by a general way.
In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimizat...
详细信息
In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimization problems involving a generalized oriented distance function have been considered. Characterization of u-minimal solutions of (u-SOP) in terms of solutions of these scalar optimization problems have been obtained. Finally, equivalence of well-posedness of (u-SOP) with well-posedness of these scalar optimization problems have been established.
In this paper, by proposing a new type of generalized C-quasiconvexity for the set-valued mappings and using the nonlinear scalarization function and its properties, without assumption of monotonicity and boundedness,...
详细信息
In this paper, by proposing a new type of generalized C-quasiconvexity for the set-valued mappings and using the nonlinear scalarization function and its properties, without assumption of monotonicity and boundedness, some existence results of the solutions for the symmetric vector equilibrium problems and symmetric scalar equilibrium problems are established. Moreover, the convexity of solution sets is also investigated. Finally, some examples to support our results are provided.
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two ...
详细信息
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
暂无评论