A Modified Liu and Storey Conjugate Gradient Method for Large Scale Unconstrained Optimization Problems
Round 1
Reviewer 1 Report
Please see the attachment.
Comments for author File: 
Comments.pdf
Author Response
Dear...
Thank you very much for these comments which really improve our manuscript.
Author Response File: 
Author Response.docx
Reviewer 2 Report
1, On Page 5, Line 118, Eq(16), what is the motivation of the CG parameter $\beta_k^{LS+}$？Why you consider to introduce the scalar $\mu_k$, please give a clear explanation of the key of the above scalar.
2, Since the new method is based on LS and DL method, compare with them, what is the main superiority over the latter two methods? The author should compare the new method with them computationally.
Author Response
Dear...
Thank you very much for these comments which really improve our manuscript.
Author Response File: Author Response.docx
Reviewer 3 Report
First of all, I want to say that the work which has been performed by the authors is interesting and could be shared with other specialists via the Journal. The main result of the paper that can be used in some practical applications is the new variation of the well-known conjugate gradient methods. The authors state that their method has a global convergence property that is very important when solving some nonlinear inverse problems.
I believe that any method that addresses global convergence issues is worthy of consideration for publication. However, I must state that there is at least one major flaw, which is contained in the main theorem of this work (Theorem 3.4). I want to mention that the ``global convergence'' means that the method can find the global minimum, as opposed to the ``local convergence'' of the conventional minimization techniques (for examples, DOI: 10.1088/1361-6420/ab9893, 10.1137/070711414). However, it follows from the formulation of the theorem that the proposed method finds only a local minimum. Thus the incorrect use of the term ``global convergence'' must be corrected.
Author Response
Dear...
Thank you very much for these comments which really improve our manuscript.
Author Response File: Author Response.docx
Reviewer 4 Report
Authors propose a robust CG method. The new method is constructed based on Liu and Storey method to overcome the convergence problem and descent property for this method. The new modified method satisfies the global convergence properties and the sufficient decent condition under some assumptions. The numerical results show that the new method outperform recent CG methods such CG-Descent5.3, the numerical results includes the number of iterations, and CPU time.
The paper is interesting and correct however I am not sure if the novelty of the paper enough to be published. I suggest the authors to highlight its novelty more in the introduction.
Paper needs an English and editing check. For example in conclusion "the the", etc.
Author Response
Dear...
Thank you very much for these comments which really improve our manuscript.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Although the authors revised the whole manuscript, the proposed method make little contribution the field of CG method.
Author Response
Dear reviewer ...
Thank you very much for these comments which improve our paper.
Author Response File: Author Response.docx
Reviewer 3 Report
The authors have successfully corrected the major flaw. I no longer have comments on the main content of the article.
As minor fixes, I suggest (but not necessary) indicating in the introduction (or conclusion) that the proposed method is of great interest in solving nonlinear coefficient inverse problems for partial differential equations (for examples, DOI: 10.1088/1361-6420/ab8483, 10.1088/1361-6420/ab2aab,
10.1088/1361-6420/ab9893, 10.3390/a13040098, 10.3390/math9040342, 10.1016/j.cnsns.2021.105824, 10.1088/0266-5611/21/1/017, 10.1137/070711414). This remark can be done in order to clarify the state of the art and a review of possible applications of the proposed algorithms.
Author Response
Dear Reviewer ...
Thank you very much for these comments which improve our paper. I attached the corrections.
Author Response File: Author Response.docx
