弱广义向量拟似变分不等式解的存在性

研究拓扑向量空间上弱广义向量拟似变分不等式解的存在性问题.与Khaliq和Rashid等在单调或伪单调假设条件下,利用KKM定理证明解的存在性不同,在集值映射是非空凸值映射并且有开下截口的条件下,利用Fan-Browder不动点原理证明解的存在性.     

Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators

Noncompact convexificators, which provide upper convex and lower concave approximations for a continuous function, are defined. Various calculus rules, including extremality and mean-value properties, are presented. Regularity conditions are given for convexificators to be minimal. A characterization of quasiconvexity of a continuous function is obtained in terms of the quasimonotonicity of convexificators.     

Semicontinuity and Quasiconvex Functions

Criteria are derived for quasiconvex functions under lower semicontinuity and upper semicontinuity conditions. The results thus obtained generalize earlier results for convex functions. We also give new conditions under which a given function is r-convex in the sense given by Avriel.     

On Vector Quasi-Equilibrium Problems with Set-Valued Maps

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.     

拓扑空间中锥拟凸映射多目标优化问题有效解集的连通性

本文研究拓扑空间中锥拟凸多目标优化问题的有效解集的连通性．在目标映射是上连续和拟凸(次严格拟凸)的条件下，证明了锥弱有效(有效)解集是连通的.进一步，在是连续和强拟凸的条件下，证明了锥有效解集是路连通的.     

一个标量泛函的研究及其在集值优化问题中的应用

本文在K条件下,研究了所给标量泛函的连续性和拟凸性,并利用该标量泛函,将集值优化问题转化为均衡问题,进而研究了含约束的集值优化问题弱充分解的存在性和拟集值优化问题强逼近解映射的上半连续性与下半连续性.与最近的文献相比,我们的方法是新的,条件和结论也更具一般性.     

拓扑向量空间中锥拟凸映射的若干性质

本文针对拓扑向量空间中锥拟凸映射类 ,利用Minkowski泛函研究其若干性质 ,Karamardian定理是本文所得结论的一个特例 .     

Beyond polyconvexity: an existence result for a class of quasiconvex hyperelastic materials

This article contains an existence result for a class of quasiconvex stored energy functions satisfying the material non‐interpenetrability condition, which primarily obstructs applying classical techniques from the vectorial calculus of variations to nonlinear elasticity. The fundamental concept of reversibility serves as the starting point for a theory of nonlinear elasticity featuring the basic duality inherent to the Eulerian and Lagrangian points of view. Motivated by this concept, split‐quasiconvex stored energy functions are shown to exhibit properties, which are very alluding from a mathematical point of view. For instance, any function with finite energy is automatically a Sobolev homeomorphism; existence of minimizers can be readily established and first variation formulae hold. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimality conditions in multiobjective differentiable programming

A theorem stated in Ref. 1 is corrected.     

Optimality conditions in multiobjective differentiable programming

Necessary conditions not requiring convexity are based on the convergence of a vector at a point and on Motzkin's theorem of the alternative. A constraint qualification is also involved in the establishment of necessary conditions. Three theorems on sufficiency require various levels of convexity on the component of the functions involved, and the equality constraints are not necessarily linear. Scalarization of the objective function is used only in the last sufficiency theorem.The author is thankful to the unknown referce whose comments improved the quality of the paper.