Hamilton–Jacobi equation
https://openalex.org/C2778860007
https://www.wikidata.org/wiki/Q1060137
Algorithm
https://openalex.org/C11413529
https://www.wikidata.org/wiki/Q8366
Curvature
https://openalex.org/C195065555
https://www.wikidata.org/wiki/Q214881
Mathematics
https://openalex.org/C33923547
https://www.wikidata.org/wiki/Q395
Mean curvature flow
https://openalex.org/C127813850
https://www.wikidata.org/wiki/Q6803617
Function (biology)
https://openalex.org/C14036430
https://www.wikidata.org/wiki/Q3736076
Conservation law
https://openalex.org/C3445786
https://www.wikidata.org/wiki/Q205805
Mean curvature
https://openalex.org/C175017881
https://www.wikidata.org/wiki/Q1318998
Mathematical analysis
https://openalex.org/C134306372
https://www.wikidata.org/wiki/Q7754
Stating purpose of the current research with reference to gaps or issues in the literature
The aim of our work was to fill these gaps in the existing literature by … 
[INST] Please produce a sentence from the paper. The sentence should not mention the title of the paper, rather it be extracted from the Introducing Work section of the paper.
Please provide one singular full sentence from the paper that serves the function provided, using the example as guidance. Be specific, using relevant terminology from the paper.
Refrain from vague or generic statements. Finally produce a search query in the form of a question targeted towards the knowledge contained therein. 
You must output json with the structure of {'Sentence': sentence, 'Query': query}.
Field: "Algorithm".
Paper: "On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming"
Function: "Stating purpose of the current research with reference to gaps or issues in the literature".
Example Sentence: "The aim of our work was to fill these gaps in the existing literature by … ". [/INST]