共查询到20条相似文献,搜索用时 15 毫秒
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We consider a general control problem which includes, as particular cases, Bolza, Lagrange and Mayer problems. We show that it can be reduced to a free problem and we give sufficient conditions for the existence of a minimum over all absolutely continuous arcs with values in a reflexive, separable Banach space. A regularization result is also proved and an application to explicit control problems is considered.This work was supported by the Laboratorio per la Matematica Applicata del C. N. R.-Istituto di Matematica della Università di Genova. 相似文献
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This work is concerned with nonlinear differential equations with nonlocal conditions in Banach spaces. Using the theory of nonlinear semigroups and approximation techniques, a new existence result is obtained, for integral solutions. An example is also given to illustrate the abstract theory. 相似文献
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We prove a weak convergence theorem for generalized nonexpansive mappings in uniformly convex Banach spaces whose dual has the Kadec–Klee property. This theorem is connected with a famous convergence theorem for nonexpansive mappings proved by Reich in 1979. 相似文献
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In this paper, we first give a simple proof of the decomposition theorem in Alber (Field Inst. Comm. 25 (2000) 77) and then present a new decomposition of arbitrary elements in reflexive strictly convex and smooth Banach spaces. As applications of the decomposition theorem, we give the representations of the metric projection operator for some kind of closed convex sets. Finally, we provide a sufficient condition under which the generalized projection operator coincides with the metric projection operator. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(2):826-838
The purpose of this paper is the presentation of a new extragradient algorithm in 2‐uniformly convex real Banach spaces. We prove that the sequences generated by this algorithm converge strongly to a point in the solution set of split feasibility problem, which is also a common element of the solution set of a generalized equilibrium problem and fixed points of of two relatively nonexpansive mappings. We give a numerical example to investigate the behavior of the sequences generated by our algorithm. 相似文献
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We deal with a generalization of the proximal-point method and the closely related Tikhonov regularization method for convex optimization problems. The prime motivation behind this is the well-known connection between the classical proximal-point and augmented Lagrangian methods, and the emergence of modified augmented Lagrangian methods in recent years. Our discussion includes a formal proof of a corresponding connection between the generalized proximal-point method and the modified augmented Lagrange approach in infinite dimensions. Several examples and counterexamples illustrate the convergence properties of the generalized proximal-point method and indicate that the corresponding assumptions are sharp. 相似文献
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Prapairat JunlouchaiSomyot Plubtieng 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(3):999-1004
In this paper, we prove the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over compact convex subsets in a reflexive Banach space with a Fréchet differentiable norm. Moreover, we give some conditions that guarantee the existence of solutions of generalized variational inequality for upper semicontinuous multivalued mappings with compact contractible values over unbounded closed convex subsets. The result obtained in this paper improves and extends the recent ones announced by Yu and Yang [J. Yu, H. Yang, Existence of solutions for generalized variational inequality problems, Nonlinear Anal., 71 (2009) e2327-e2330] and many others. 相似文献
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Arkady Aleyner 《Journal of Mathematical Analysis and Applications》2008,343(1):427-435
We establish convergence theorems for two different block-iterative methods for solving the problem of finding a point in the intersection of the fixed point sets of a finite number of nonexpansive mappings in Hilbert and in finite-dimensional Banach spaces, respectively. 相似文献
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Privatdozent Dr. K. Ritter 《Probability Theory and Related Fields》1970,14(4):257-263
Summary The concept of duality plays an important role in mathematical programming and has been studied extensively in a finite dimensional Eucledian space, (see e.g. [13, 4, 6, 8]). More recently various dual problems with functionals as objective functions have been studied in infinite dimensional vector spaces [5, 7, 1, 10, 12].In this note we consider a nonlinear minimization problem in a partially ordered Banach space. It is assumed that the objective function of this problem is given by a (nonlinear) operator and that its feasible domain is defined by a system of (nonlinear) operator inequalities. In analogy to the finite dimensional case we associate with this minimization problem a dual maximization problem which is defined in the Cartesian product of certain Banach spaces. It is shown that under suitable assumptions the main results of the finite dimensional duality theory can be extended to this general case. This extension is based on optimality conditions obtained in [11]. 相似文献
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《Applied Mathematics Letters》2007,20(8):908-912
We consider the penalty method for solving generalized nonlinear variational inequalities. We obtain some existence theorems for the variational inequalities by the penalty method in reflexive real Banach spaces. 相似文献
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We study the convergence of an iterative algorithm for finding common fixed points of finitely many Bregman firmly nonexpansive
operators in reflexive Banach spaces. Our algorithm is based on the concept of the so-called shrinking projection method and
it takes into account possible computational errors. We establish a strong convergence theorem and then apply it to the solution
of convex feasibility and equilibrium problems, and to finding zeroes of two different classes of nonlinear mappings. 相似文献
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In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency. 相似文献
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A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the approximate solutions of the generalized mixed equilibrium problems (GMEP) and bilevel generalized mixed equilibrium problems (BGMEP) involving set-valued mappings is introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions. By using auxiliary principle technique, new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP is suggested and analyzed. Strong convergence of the iterative sequences generated by the proposed algorithms is proved under quite mild assumptions. These results are new and generalize some recent results in this field. 相似文献