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121.
We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.The authors thank Dr. T. D. Phuong, Dr. T. X. D. Ha, and the referees for helpful comments and suggestions. 相似文献
122.
Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized
subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions
for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many
other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative
due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.
相似文献
123.
In this paper, a gap function for a system of vector equilibrium problems is introduced and studied. Some necessary and sufficient
conditions for the system of vector equilibrium problems are established. Characterizations of the solutions set for the system
of vector equilibrium problems are also derived. Furthermore, some existence results of solutions for the system of vector
equilibrium problems are proved.
This work was supported by the National Natural Science Foundation of China, the Youth Foundation, Sichuan Education Department
of China, the National Natural Science Foundation, Sichuan Education Department of China (2004C018), and a grant from the
National Science Council of ROC. 相似文献
124.
Michal Fećkan 《Applications of Mathematics》1997,42(5):369-393
Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems. 相似文献
125.
设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的非空闭凸子集而且是E的非扩张收缩核.设T:D→E是具有序列{kn}[1,∞),limn→∞kn=1的非自渐近非扩张映象,P:E→D是一非扩张保核收缩.本文证明了,在一定条件下,由修正的Reich-Takahashi迭代法(1.2)和(1.3)式定义的迭代序列{xn}强收敛于非自渐近非扩张映象T的不动点. 相似文献
126.
A new test for strict monotonicity of the regression function is proposed which is based on a composition of an estimate of
the inverse of the regression function with a common regression estimate. This composition is equal to the identity if and
only if the “true” regression function is strictly monotone, and a test based on an L
2-distance is investigated. The asymptotic normality of the corresponding test statistic is established under the null hypothesis
of strict monotonicity.
相似文献
127.
We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters ( and ), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping originates from the analysis of birational transformations obtained from very simple algebraic calculations, namely taking the inverse of q × q matrices and permuting some of the entries of these matrices. It has been seen to yield weak chaos and integrability. We have found new integrable cases of this Cremona transformation, corresponding to the values of = 0 when
, besides the already known values = 0 and = −1, and also arbitrary when = 0. For these cases, one has a foliation of the parameter space in elliptic curves. We give the equations of these elliptic curves. Based on this very example we show how one can find these integrability cases of the Cremona transformation and actually integrate it using a method based on the systematic study of the finite-order conditions of the Cremona transformation. The method is shown to be efficient and straightforward. The various integrability cases are revisited using many different representations of this very mapping (birational transformations, recursion in one variable, …). 相似文献
128.
R-linear convergence of the Barzilai and Borwein gradient method 总被引:4,自引:0,他引:4
Combined with non-monotone line search, the Barzilai and Borwein(BB) gradient method has been successfully extended for solvingunconstrained optimization problems and is competitive withconjugate gradient methods. In this paper, we establish theR-linear convergence of the BB method for any-dimensional stronglyconvex quadratics. One corollary of this result is that theBB method is also locally R-linear convergent for general objectivefunctions, and hence the stepsize in the BB method will alwaysbe accepted by the non-monotone line search when the iterateis close to the solution. 相似文献
129.
Jörn Loviscach 《Journal of statistical physics》1994,75(1-2):189-213
Strongly chaotic systems (e.g., piecewise expanding mappings) exhibit diffusion-like behavior in the sense of central limit theorems. To find more precise statements about the similarity to probabilistic diffusion, we study how the evolution of probability densities underd-dimensional piecewise expanding mappings can be modeled by Markov processes with smooth transition probabilities (such as diffusion processes). Our results can be viewed as a special type of local limit theorem. 相似文献
130.
A. Djoudi 《Journal of Mathematical Analysis and Applications》2007,329(1):31-45
We prove a common fixed point theorem of Gregus type for four mappings satisfying a contractive condition of integral type in metric spaces using the concept of weak compatibility which generalizes Theorem 2 of [A. Djoudi, L. Nisse, Gregus type fixed points for weakly compatible mappings, Bull. Belg. Math. Soc. 10 (2003) 369-378] and other papers. We prove also common fixed point theorems of Gregus type using a strict contractive condition of integral type, a property (E.A) and a common property (E.A) introduced by [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181-188] and [W. Liu, J. Wu, Z. Li, Common fixed points of single-valued and multi-valued maps, Int. J. Math. Math. Sci. 19 (2005) 3045-3055], respectively. 相似文献