A Fixed-Point Subgradient Splitting Method for Solving Constrained Convex Optimization Problems
Round 1
Reviewer 1 Report
In this paper the author presents a fixed-point subgradient splitting method for minimizing the sum of convex functions over the sets of all fixed points of nonlinear operators.
The result is obtained by considering some specific suitable assumptions on the step sizes.
Some convergence properties of the proposed method are presented and the applications of that scheme to known problems in the literature are discussed.
Also, (in section 6) numerical experiments are given to sustain the effectiveness of the theoretical result.
I consider that this paper contains new and interesting results, so that, I'll recomand it for publication.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, authors present a simple fixed-point subgradient splitting method, whose main feature is the combination of the subgradient method with the hybrid steepest descent method relating to a nonlinear operator. They carry out a good introduction. The proposed method and results are representative and can be of considerable interest.
Why did authors choose this particular journal, since the “symmetry” is not mentioned in the article.
What is the novelty of the article?
The abstract should briefly explain the problem that has been tried to solve, how it has been solved and the conclusions or results obtained. Along with the title, it is the first section that researchers read when they search for articles related to their research topic.
On the next paragraph in page 3: “On the other hand, in the recent decade, the split common fixed point problem [?, 11] turns out to be one of the attractions among several nonlinear problems due to its widely applications in many image and signal processing problems.” Reference is missed.
On the next paragraph in page 3: “The paper is organized as follows. After recalling and introducing some useful notions and tools in section 2, we present our algorithm and its convergence properties in section 3. In section 5 we discuss in detail some remarkably practical applications, while section 6 describes the results of numerical experiments on fused lasso like problem. Finally, the conclusions are given in section 7.” Section 4 is not mencioned.
In section 2 there are only two references. I think is neccesary more references since it is the section where authors must explain the current advances in the subject in question.
Why problem 7 is before that problem 6?
I have no objections concerning the pure mathematical aspects of the paper.
References 9, 11 and 15 are not mentioned in the text.
References should be placed in order of appearance in the text. Authors must use the Microsoft Word template or LaTeX template to prepare their manuscript. See https://www.mdpi.com/journal/symmetry/instructions
It is convenient to add more current references.
For all this, I recommends the paper to be accepted with mayor revision in Symmetry journal.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Accept
