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1.
Proximal point algorithms (PPA) are attractive methods for monotone variational inequalities. The approximate versions of PPA are more applicable in practice. A modified approximate proximal point algorithm (APPA) presented by Solodov and Svaiter [Math. Programming, Ser. B 88 (2000) 371–389] relaxes the inexactness criterion significantly. This paper presents an extended version of Solodov–Svaiter's APPA. Building the direction from current iterate to the new iterate obtained by Solodov–Svaiter's APPA, the proposed method improves the profit at each iteration by choosing the optimal step length along this direction. In addition, the inexactness restriction is relaxed further. Numerical example indicates the improvement of the proposed method.  相似文献   
2.
In this paper, by means of the method of upper and lower solutions and monotone iterative technique, the existence of maximal and minimal solutions of the boundary value problems for first order impulsive delay differential equations is established.  相似文献   
3.
Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained.  相似文献   
4.
In this paper the classical theorem of Zareckii about regular relations is generalized and an intrinsic characterization of regularity is obtained. Based on the generalized Zareckii theorem and the intrinsic characterization of regularity, the authors give a characterization of monotone normality of ordered spaces. A new proof of the Urysohn-Nachbin lemma is presented which is quite different from the classical one.  相似文献   
5.
We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.  相似文献   
6.
The paper deals with complementarity problems CP(F), where the underlying functionF is assumed to be locally Lipschitzian. Based on a special equivalent reformulation of CP(F) as a system of equationsφ(x)=0 or as the problem of minimizing the merit functionΘ=1/2∥Φ2 2 , we extend results which hold for sufficiently smooth functionsF to the nonsmooth case. In particular, ifF is monotone in a neighbourhood ofx, it is proved that 0 εδθ(x) is necessary and sufficient forx to be a solution of CP(F). Moreover, for monotone functionsF, a simple derivative-free algorithm that reducesΘ is shown to possess global convergence properties. Finally, the local behaviour of a generalized Newton method is analyzed. To this end, the result by Mifflin that the composition of semismooth functions is again semismooth is extended top-order semismooth functions. Under a suitable regularity condition and ifF isp-order semismooth the generalized Newton method is shown to be locally well defined and superlinearly convergent with the order of 1+p.  相似文献   
7.
本文对一类重要的混合单调算子证明了不动点的存在、唯一与逼近定理,并应用于研究动态规划中泛函方程的正解问题.  相似文献   
8.
The purpose of this paper is to study the existence problem of solutions and perturbation problem for some kind of variational inequalities with monotone operators in nonreflexive Banach spaces, and to obtain some results.  相似文献   
9.
On the characterisation of paired monotone metrics   总被引:1,自引:1,他引:0  
Hasegawa and Petz introduced the notion of paired monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the paired family. In this paper we show that the characterisation theorem holds true under hypotheses that are more general than those used in the above quoted references.  相似文献   
10.
In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.  相似文献   
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