Self-Adaptive and Relaxed Self-Adaptive Projection Methods for Solving the Multiple-Set Split Feasibility Problem

Self-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.

A Splitting-relaxed Projection Method for Solving the Split Feasibility Problem

The split feasibility problem (SFP) is to find x ∈ C so that Ax ∈ Q, where C is a nonempty closed convex subset of Rn, Q is a nonempty closed convex subset of Rm, and A is a matrix from Rn into Rm. One of successful methods for solving the SFP is Byrne’s CQ algorithm. However, to carry out the CQ algorithm, it is required that the closed convex subsets are simple and that the matrix norm is kno...

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...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Modified Halfspace-Relaxation Projection Methods for Solving the Split Feasibility Problem