An Explicit Method for the Split Feasibility Problem with Self-Adaptive Step Sizes
نویسندگان
چکیده
منابع مشابه
An Explicit Method for the Split Feasibility Problem with Self-Adaptive Step Sizes
and Applied Analysis 3 Next we adopt the following notation: i xn → x means that xn converges strongly to x; ii xn ⇀ x means that xn converges weakly to x; iii ωw xn : {x : ∃xnj ⇀ x} is the weak ω-limit set of the sequence {xn}. Recall that a function f : H → R is called convex if f ( λx 1 − λ y ≤ λf x 1 − λ fy, 2.4 for all λ ∈ 0, 1 and ∀x, y ∈ H. It is known that a differentiable function f is...
متن کاملSelf-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem
and Applied Analysis 3 half-spaces, so that the algorithm is implementable. We need not estimate the Lipschitz constant and make a sufficient decrease of the objection function at each iteration; besides, these projection algorithms can reduce to the modifications of the CQ algorithm 6 when the MSSFP 1.1 is reduced to the SFP. We also show convergence the algorithms under mild conditions.
متن کاملAn algorithm for the split-feasibility problems with application to the split-equality problem
In this paper, we study the split-feasibility problem in Hilbert spaces by using the projected reflected gradient algorithm. As applications, we study the convex linear inverse problem and the split-equality problem in Hilbert spaces, and we give new algorithms for these problems. Finally, numerical results are given for our main results.
متن کاملRegularized Methods for the Split Feasibility Problem
and Applied Analysis 3 However, 1.8 is, in general, ill posed. So regularization is needed. We consider Tikhonov’s regularization min x∈C fα : 1 2 ∥I − PQ ) Ax ∥∥2 1 2 α‖x‖, 1.9 where α > 0 is the regularization parameter. We can compute the gradient ∇fα of fα as ∇fα ∇f x αI A∗ ( I − PQ ) A αI. 1.10 Define a Picard iterates x n 1 PC ( I − γA∗I − PQ ) A αI )) x n 1.11 Xu 20 shown that if the SFP...
متن کاملLagrangian Relaxation Method for the Step fixed-charge Transportation Problem
In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2012
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2012/432501