Banach空间中的一阶脉冲积分-微分方程边值问题

讨论了抽象空间中的一阶脉冲积分-微分方程的边值问题，利用上下解讨论了解的存在性．     

向量集值优化超有效解的对偶问题

借助于Contingent切锥和集值映射的上图而引入的有关集值映射的Contingent切导数，对约束集值优化问题的超有效解建立了最优性Kuhn Tucker必要及充分性条件,借此建立了向量集值优化超有效解的Wolfe型和Mond Weir型对偶定理.     

The generalized linear complementarity problem revisited

Given a vertical block matrixA, we consider in this paper the generalized linear complementarity problem VLCP(q, A) introduced by Cottle and Dantzig. We formulate this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke. Our formulation helps in extending many well-known results in linear complementarity to the generalized linear complementarity problem. We also show that the class of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as the class of equivalent square matrices which Lemke's algorithm can process. We also present some degree-theoretic results on a vertical block matrix.     

Exact penalties and sufficient conditions for optimality in nonsmooth optimization

Under certain sufficient conditions for strict local optimality in a mathematical program, it is well known that a number of non-differentiable penalty functions are locally exact. With sufficient conditions involving the contingent derivative, it is shown that this local exactness is valid for programs whose objective and constraint functions need not be differentiable or even continuous. The author is grateful to the referees for their helpful comments.     

Optimality condition: Constraint regularization

Necessity and sufficiency conditions are given for the existence of a finite set of redundant constraints which together with a given set of constraints in an optimization problem satisfy the Kuhn—Tucker, and the Guignard Constraint qualifications when the original set of constraints fails to satisfy either or both of them.This work was carried out at the Department of Statistics, University College of Wales, Aberystwyth while the author was sponsored by the Commonwealth Scholarship Commission in the United Kingdom, through the Department of Statistics, University of Nigeria, Nsukka.     

Full Nuclear Cones and a Relation Between Strong Optimization and Pareto Efficiency

In this paper we present some new and pertinent connections between the Strong Optimization and the Approximate Pareto type Efficiency, in particular, with the usual Vector Optimization, at first in the Ordered Vector Spaces by the natural Convex Cones and, afterwards, in the Ordered Hausdorff Locally Convex Spaces. The main result is obtained considering the notion of full nuclear cone. Our results, is related to an appropriate scalarization method Mathematics Subject Classification (2000). 90C29     

带非线性边界条件的二阶奇异微分系统正解的存在性

研究了带非线性边界条件的二阶奇异微分系统边值问题-u″=ΛG(t)F(u),0<t<1,u(0)=0,u'(1)+C(u(1))u(1)=0正解的存在性,其中u=(u1,u2,?,un)T,G(t)=diag[g1(t),g2(t),?,gn(t)],且gi(t)(i=1,2,?,n)在t=0处允许有奇性F(u)=(f1(u),f2(u),?,fn(u))T,C=diag(c1,c2,?,cn),Λ=diag(λ1,λ2,?,λn),λi(i=1,2,?,n)为正参数。在非线性项F分别满足超线性、次线性和渐近线性的增长条件下,运用锥拉伸与压缩不动点定理获得了该问题正解的存在性结论。     

On convergence of closed convex sets

In this paper we introduce a convergence concept for closed convex subsets of a finite-dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé-Kuratowski convergence and with scalar convergence. In fact, we show that a sequence (An)_n∈NC-converges to A if and only if the corresponding support functions converge pointwise, except at relative boundary points of the domain of the support function of A, to the support function of A.     

Tangent cones and C1 regularity of definable sets

Let $X?{\mathbb{R}}^n$ be a connected locally closed set which is definable in an o-minimal structure. We prove that the following three statements are equivalent: (i) X is a $C^1$ manifold, (ii) the tangent cone and the paratangent cone of X coincide at every point in X, (iii) for every $x\in X$, the tangent cone of X at the point x is a k-dimensional linear subspace of ${\mathbb{R}}^n$ (k does not depend on x) varies continuously in x, and the density $\theta (X,x)<3/2$.