具集值映射的广义强向量拟均衡问题

讨论了一类具集值映射的广义强向量拟均衡问题（GSVQEP）解的存在性.利用连续选择定理和不动点定理,在没有任何单调性假设下得到了GSVQEP解的存在性定理.     

Regularity of almost minimizers of quasi-convex variational integrals with subquadratic growth

We prove a small excess regularity theorem for almost minimizers of a quasi-convex variational integral of subquadratic growth. The proof is direct, and it yields an optimal modulus of continuity for the derivative of the almost minimizer. The result is new for general almost minimizers, and in the case of absolute minimizers it considerably simplifies the existing proof. Mathematics Subject Classification (2000) 49N60, 26B25     

Conjugaison par tranches et dualitë de toland

A level set duality scheme analoguous to Toland's one is developed. In particular, his formula on the difference of two functions finds its level-set analogue. In this way, new couples of dual optimization problems are obtained. Applications to the maximization of functions which level sets are P-closed (where Pis a not necessarily topological closure) are shown.     

二层广义凸规划及其性质

讨论了二层规划的性质 ,在一些凸性和广义凸性假设下 ,讨论了下层极值函数和上层目标函数的凸性、拟凸性和连续性性质 ,获得了五个定理 ,并予以证明 .     

Generalized convexities of lower semicontinuous functions

In this paper a general theorem on the replacement of the condition “for all λ” in the definition of generalized convexity properties of lower semicontinuous functions by the condition “there exists a λ” is shown. This result can be applied to a number of special kinds of convexity and completes, for instance, studies of Behbikgeb concerning (explicitly) quasiconvex functions.     

二层不变凸规划的性质

在G^ateaux可微和不变凸假设下,给出了二层广义凸规划的凸性,推广了二层规划的若干结果.     

A stability result in quasi-convex programming

Combining a result on the lower semicontinuity of the intersection of two convex-valued multifunctions and the level set approach of epi-convergence, we obtain results on the epi-upper semicontinuity of the supremum and the sum of two families of quasi-convex functions. As a consequence, we give some condition ensuring the stability of a quasi-convex program under a perturbation of the objective functions and the constraint sets.     

On system of generalized vector variational inequalities

In this paper, we introduce a new system of generalized vector variational inequalities with variable preference. This extends the model of system of generalized variational inequalities due to Pang and Konnov independently as well as system of vector equilibrium problems due to Ansari, Schaible and Yao. We establish existence of solutions to the new system under weaker conditions that include a new partial diagonally convexity and a weaker notion than continuity. As applications, we derive existence results for both systems of vector variational-like inequalities and vector optimization problems with variable preference.     

An Algorithm for Detecting Directional Quasi-Convexity

Directional Quasi-Convexity (DQC) is a sufficient condition for Nekhoroshev stability, that is, stability for finite but very long times, of elliptic equilibria of Hamiltonian systems. The numerical detection of DQC is elementary for system with three degrees of freedom. In this article, we propose a recursive algorithm to test DQC in any number n4 of degrees of freedom.