共查询到20条相似文献,搜索用时 15 毫秒
1.
Stability of Slopes and Subdifferentials 总被引:1,自引:0,他引:1
We show that the slope introduced by DeGiorgi, Marino and Tosques in 1980 is stable (in a sense to be made precise) with respect to the variational convergence introduced by the authors in 2000. Applications to the stability of subdifferentials are derived, including a further characterization of slice-convergence of convex functions in terms of set convergence of enlargements of their subdifferentials. 相似文献
2.
In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established. 相似文献
3.
In this paper relationships between Pareto points and saddle points are studied in convex and nonconvex multiple objective programming. The analysis is based on partitioning the index sets of objectives and constraints and splitting the original problem into subproblems having a special structure. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. In the nonconvex case, a saddle point characterization of Pareto points is possible under assumptions that guarantee existence of Pareto points and stability conditions of single objective problems. Essentially, these conditions are not stronger than those in analogous results for single objective programming.This research was partially supported by ONR Grant N00014-97-1-784AMS Subject Classification: 90C29, 90C26 相似文献
4.
6.
7.
In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional
system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and incoexistence of the
1-heteroclinic loop with three or two saddle points, 1-homoclinic orbit and 1-periodic orbit near Γ are obtained. Meanwhile,
the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the
case for heteroclinic loop with l saddle points.
Received January 4, 2001, Accepted July 3, 2001. 相似文献
8.
Most standard textbooks about asymptotic approximations of integrals do not give explicit formulas for the coefficients of
the asymptotic methods of Laplace and saddle point. In these techniques, those coefficients arise as the Taylor coefficients
of a function defined in an implicit form, and the coefficients are not given by a closed algebraic formula. Despite this
fact, we can extract from the literature some formulas of varying degrees of explicitness for those coefficients: Perron’s
method (in Sitzungsber. Bayr. Akad. Wissensch. (Münch. Ber.), 191–219, 1917) offers an explicit computation in terms of the derivatives of an explicit function; in (de Bruijn, Asymptotic Methods in
Analysis. Dover, New York, 1950) we can find a similar formula for the Laplace method which uses derivatives of an explicit function. Dingle (in Asymptotic
Expansions: Their Derivation and Interpretation, Academic Press, New York, 1973) gives the coefficients of the saddle point method in terms of a contour integral. Perron’s method is rediscovered in (Campbell
et al., Stud. Appl. Math. 77:151–172, 1987), but they also go farther and compute the above mentioned derivatives by means of a recurrence. The most recent contribution
is (Wojdylo, SIAM Rev. 48(1):76–96, 2006), which rediscovers the Campbell, Fr?man and Walles’ formula and rewrites it in terms of Bell polynomials (in the Laplace
method) using new ideas of combinatorial analysis which efficiently simplify and systematize the computations. In this paper
we continue the research line of these authors. We combine the more systematic version of the saddle point method introduced
in (López et al., J. Math. Anal. Appl. 354(1):347–359, 2009) with Wojdylo’s idea to derive a new and more explicit formula for the coefficients of the saddle point method, similar to
Wojdylo’s formula for the coefficients of the Laplace method. As an example, we show the application of this formula to the
Bessel function. 相似文献
9.
Z. K. Xu 《Journal of Optimization Theory and Applications》1997,94(3):739-746
Recently, Li (Ref. 1) obtained a saddle-point result for a general class of nonconvex optimization problems with inequality constraints, by using a transformation equivalent to taking the pth power of the objective function and the constraints, under several conditions. In this paper, we show that, by an equivalent transformation, using the pth power of the constraints or using the pth power of the objective function and the constraints, the same result can be obtained under much weaker and reasonable conditions. Also, our results can be extended to the problem in which equality and inequality constraints are involved. 相似文献
10.
11.
Generalized Semicontinuity and Existence Theorems for Cone Saddle Points 总被引:11,自引:0,他引:11
This paper is concerned with existence theorems for generalized saddle points (cone saddle points) of vector-valued functions.
A concept of lower semicontinuity for vector-valued functions is introduced and its properties are investigated. Previous
results of the author are extended by using the lower semicontinuity.
Accepted 26 April 1996 相似文献
12.
13.
J. Y. Fu 《Journal of Optimization Theory and Applications》2006,128(3):605-619
In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi 相似文献
14.
本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理. 相似文献
15.
16.
17.
This paper is devoted to considering the coderivatives of the generalized perturbation maps in general Banach spaces. Under some mild conditions, the upper estimate of coderivatives of the generalized perturbation maps are obtained. Their exact calculus rules are obtained under some additional conditions. Furthermore, the generalized perturbation maps are shown to be differentiably regular under some strong conditions. 相似文献
18.
本文利用Moser扭转定理证明了一类Duffing方程x″ 9(x)=e(t)的Lagrange稳定性,其中e(t)以1为周期,9:R→R具有下列性质:当x≥d0时,9(x)是超线性的;当x≤-d0时,9(x)是次线性的,其中d0是一正常数. 相似文献
19.
Moser扭转定理在Lgrange稳定性中的应用 总被引:1,自引:0,他引:1
本文利用Moser扭转定理证明了一类Duffing方程x″+g(x)=e(t)的Lagrange稳定性,其中e(t)以1为周期,g:R→R具有下列性质:当x≥d0时,g(x)是超线性的;当x≤-d0时,9(x)是次线性的,其中d0悬一正常数. 相似文献
20.
The aim of this paper is to present an algorithm for finding a saddle point to the constrained minimax problem. The initial problem is transformed into an equivalent equality constrained problem, and then the interior point approach is used. To satisfy the original inequality constraints a logarithmic barrier function is used and special care is given to step size parameter to keep the variables within permitted boundaries. Numerical results illustrating the method are given. 相似文献