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991.
We show a modified version of Georgiev's parametric smooth variational principle, and we use it to derive new support properties of convex functions and sets. For example, our results imply that, for any proper l.s.c. convex nonaffine function h on a Banach space Y, D(∂h) is pathwise connected and R(∂h) has cardinality at least continuum. If, in addition, Y is Fréchet-smooth renormable, then R(∂h) is pathwise connected and locally pathwise connected. Analogous properties for support points and normalized support functionals of closed convex sets are proved; they extend and strengthen recent results proved by C. De Bernardi and the author for bounded closed convex sets. 相似文献
992.
In this paper, we prove a general version of Ekeland's variational principle in locally convex spaces, where perturbations contain subadditive functions of topology generating seminorms and nonincreasing functions of the objective function. From this, we obtain a number of special versions of Ekeland's principle, which include all the known extensions of the principle in locally convex spaces. Moreover, we give a general criterion for judging the density of extremal points in the general Ekeland's principle, which extends and improves the related known results. 相似文献
993.
In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating,
in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle
method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this
Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This
iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study
also the convergence of iterative sequences generated by the algorithm.
This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for
the Doctoral Program of Higher Education (20060610005), the National Natural Science Foundation of Sichuan Education Department
of China (07ZB068) and the Open Fund (PLN0703) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest
Petroleum University). 相似文献
994.
We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved
being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie subgroup
problem for Banach–Lie groups, as well as Weil’s local rigidity for homomorphisms from finitely generated groups to Banach–Lie
groups.
相似文献
995.
A sequence of inequalities which include McShane’s generalization of Jensen’s inequality for isotonic positive linear functionals and convex functions are proved and compared with results in [3]. As applications some results for the means are pointed out. Moreover, further inequalities of Hölder type are presented. 相似文献
996.
Existence theorem and algorithm for a general implicit variational inequality in Banach space 总被引:1,自引:0,他引:1
By using the generalized f-projection operator, the existence theorem of solutions for the general implicit variational inequality GIVI(T-ξ,K) is proved without assuming the monotonicity of operators in reflexive and smooth Banach space. An iterative algorithm for approximating solution of the general implicit variational inequality is suggested also, and the convergence for this iterative scheme is shown. These theorems extend the corresponding results of Wu and Huang [K.Q. Wu, N.J. Huang, Comput. Math. Appl. 54 (2007) 399–406], Wu and Huang [K.Q. Wu, N.J. Huang, Bull. Austral. Math. Soc. 73 (2006) 307–317], Zeng and Yao [L.C. Zeng, J.C. Yao, J. Optimiz. Theory Appl. 132 (2) (2007) 321–337] and Li [J. Li, J. Math. Anal. Appl. 306 (2005) 55–71]. 相似文献
997.
In this paper, we propose a new projection method for solving variational inequality problems, which can be viewed as an improvement of the method of Li et al. [M. Li, L.Z. Liao, X.M. Yuan, A modified projection method for co-coercive variational inequality, European Journal of Operational Research 189 (2008) 310-323], by adopting a new direction. Under the same assumptions as those in Li et al. (2008), we establish the global convergence of the proposed algorithm. Some preliminary computational results are reported, which illustrated that the new method is more efficient than the method of Li et al. (2008). 相似文献
998.
In this paper, we consider a system of general variational inclusions in q-uniformly smooth Banach spaces. Using proximal-point mapping technique, we prove the existence and uniqueness of solution and suggest a Mann type perturbed iterative algorithm for the system of general variational inclusions. We also discuss the convergence criteria and stability of Mann type perturbed iterative algorithm. The techniques and results presented here improve the corresponding techniques and results for the variational inequalities and inclusions in the literature. 相似文献
999.
Ronald C. King 《Journal of Combinatorial Theory, Series A》2009,116(2):314-333
The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients. 相似文献
1000.
The Perspective Reformulation generates tight approximations to MINLP problems with semicontinuous variables. It can be implemented either as a Second-Order Cone Program, or as a Semi-Infinite Linear Program. We compare the two reformulations on two MIQPs in the context of exact or approximate Branch-and-Cut algorithms. 相似文献