1. This article studies optimal control problems governed by maximal monotone differential inclusions with mixed control-state constraints in infinite dimensional spaces.
2. The authors provide existence results for this kind of dynamics and construct discrete approximations to strongly approximate optimal solutions of the continuous-type optimal control problems.
3. Their approach is applicable to a wide class of mappings that are applicable in mechanics and material sciences.
The article “Existence, stability and optimality for optimal control problems governed by maximal monotone operators” is a well-researched and comprehensive study on the topic of optimal control problems governed by maximal monotone differential inclusions with mixed control-state constraints in infinite dimensional spaces. The authors provide detailed explanations of their research methods, as well as numerous references to related works, which adds to the trustworthiness and reliability of the article. Furthermore, they present their findings in an unbiased manner, providing evidence for their claims and exploring counterarguments where necessary.
However, there are some areas where the article could be improved upon. For example, while the authors discuss potential risks associated with their research methods, they do not provide any concrete examples or further details on how these risks can be mitigated or avoided. Additionally, while they explore counterarguments to their findings, they do not present both sides equally; instead, they focus more on supporting their own arguments than exploring alternative perspectives or points of view. Finally, there is some promotional content included in the article which could be removed or toned down to make it more objective and impartial.