About the Performance of a Calculus-Based Approach to Building Model Functions in a Derivative-Free Trust-Region Algorithm

Round 1

Reviewer 1 Report

The results are nice and satisfying, and the report appears to be scientifically valid. The argument of the paper is based on a proper theory, concept, or other concepts. Furthermore, the study or comparable intellectual activity on which the publication is based must be carefully planned. The abstract simply and properly defines the substance of the article, and the results justify the interpretations and conclusions. The article demonstrates an acceptable grasp of the relevant literature in the topic and cites a sufficient number of references. This paper's topic matter is compatible with the journal's aims. As a result, I recommend that the manuscript be accepted. It is hoped that it will fully complement the current material.

Author Response

Thank-you for taking the time to review our manuscript.  We are pleased that you find it suitable for publication.

Reviewer 2 Report

This work examines a calculus-based approach to build model functions in a derivative free algorithm. This calculus-based approach can be used when the objective function considered is defined via more than one blackbox. Two versions of a derivative-free trust-region method are implemented. The first version builds model functions using a calculus-based approach and the second version builds model functions by considering the objective function directly. Numerical experiments demonstrate that the calculus-based approach provides better results in most situations and significantly better results in specific situations. In my humble opinion the article can be accepted for publication after handling the following few minor comments:

1. Elaborate more on the results depicted in all figures.

2. Comment on future extensions in this direction in the conclusion section.

3. Mention the specification of the machine used to produce all figures.

4. Proofread the whole manuscript.

 

Author Response

Thank-you for taking the time to review our manuscript.  We have revised in accordance to your recommendation.  

1.  Elaborate more on the results depicted in all figures.

  - Details have been added  at the beginning of Section 4 (Page 13).  It provides information on how to interpret the data profiles contained in Section 4.

2. Comment on future extensions in this direction in the conclusion section. 

  - Three additional  future research directions have been added in the conclusion.

3.  Mention the specification of the machine used to produce all figures.

   - Details have been added at the beginning of Section 3.3.

4. Proofread the whole manuscript.

   -Done. 

Author Response File: Author Response.pdf