250403.160209.CST revise README

Author: zaikunzhang

README.md

@@ -265,11 +265,17 @@ large constraint violation even though the starting point is feasible.
 
 ### Improvements
 
-Thanks to the improvements introduced into the new implementation, PRIMA outperforms Powell's
-original code in terms of the **number of function evaluations**, which is the standard performance
-indicator in derivative-free optimization.
+Thanks to the improvements introduced into the new implementation, PRIMA
+generally produces better solutions with less function evaluations compared with Powell's Fortran 77 implementation. This makes PRIMA preferable for if function evaluations are expensive,
+which is typically the case for [derivative-free optimization problems](https://github.com/orgs/libprima/discussions/145).
+However, if function evaluations are not the dominant cost in your application,
+The Fortran 77
+solvers are likely to be faster, as it is more efficient in terms of memory usage and flops
+thanks to the careful and unique (but unmaintained) implementation by Powell.
+
 Below are the [performance profiles](https://arxiv.org/pdf/cs/0102001.pdf)
-of the PRIMA solvers compared with Powell's implementation, the convergence tolerance being $\tau = 10^{-6}$.
+of the PRIMA solvers compared with Powell's implementation in terms of the **number of function evaluations**,
+the convergence tolerance being $\tau = 10^{-6}$.
 Roughly speaking, performance profiles plot the percentage of test problems solved against the budget,
 which is measured relative to the cost of the most efficient solver in the comparison.
 A **higher** curve indicates a **better** solver.
@@ -358,7 +364,8 @@ PRIMA has taken me significant energy and time. I will be delighted if it is use
 [its importance](https://xkcd.com/2347/) and the significant efforts it requires**.
 
 Note that PRIMA contains [bug fixes](#bug-fixes) and [improvements](#improvements) that do not exist in Powell's Fortran 77
-implementation of the solvers. Results produced by PRIMA are surely different from Powell's original solvers. Therefore,
+implementation of the solvers. Results produced by PRIMA are surely different from Powell's original solvers,
+even though the algorithms are essentially the same. Therefore,
 **it is important to point out that you are using PRIMA rather than the original solvers if you want your results to be reproducible**.
 It is wrong to pretend that PRIMA is just Powell's original solvers.
 

pyprima/README.md

@@ -16,7 +16,7 @@ Compared to Powell's Fortran 77 implementation, the modern-Fortran implementatio
 translation generally [produce better solutions with less function evaluations](https://github.com/libprima/prima#improvements),
 making them preferable for [applications with expensive function evaluations](https://github.com/orgs/libprima/discussions/145).
 However, if function evaluations are not the dominant cost in your application, the Fortran 77
-implementation are likely to be faster, as it is more efficient in terms of memory usage and flops
+solvers are likely to be faster, as it is more efficient in terms of memory usage and flops
 thanks to the careful and unique (but unmaintained) implementation by Powell.
 
 As of April 2025, only the COBYLA solver is available in this Python translation