From 1239fdc8280735d5cd8821288bda337939f39f5f Mon Sep 17 00:00:00 2001 From: James Foster <38274066+jd-foster@users.noreply.github.com> Date: Fri, 20 Sep 2024 13:14:45 +1000 Subject: [PATCH] [docs] small tweaks to Tolerances tutorial (#3830) --- docs/src/tutorials/getting_started/tolerances.jl | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/docs/src/tutorials/getting_started/tolerances.jl b/docs/src/tutorials/getting_started/tolerances.jl index fc26f80537c..7b3feed6d66 100644 --- a/docs/src/tutorials/getting_started/tolerances.jl +++ b/docs/src/tutorials/getting_started/tolerances.jl @@ -26,8 +26,9 @@ # solution is in fact optimal. However, like all numerical algorithms that use # floating point arithmetic, optimization solvers use tolerances to check # whether a solution satisfies the constraints. In the best case, the solution -# satisfies the original constraints to machine precision. In most cases, the -# solution satisfies the constraints to some very small tolerance that has no +# satisfies the original constraints to +# [machine precision](https://en.wikipedia.org/wiki/Machine_epsilon). In most cases, +# the solution satisfies the constraints to some very small tolerance that has no # noticeable impact on the quality of the optimal solution. In the worst case, # the solver can return a "wrong" solution, or fail to find one even if it # exists. (In the last case, the solution is wrong only in the sense of user @@ -284,7 +285,7 @@ primal_feasibility_report(model, Dict(x => 1.0, y => 0.0)) # ### Why you shouldn't use a small tolerance # Just like primal feasibility tolerances, using a smaller value for the -# integrality tolerance and lead to greatly increased solve times. +# integrality tolerance can lead to greatly increased solve times. # ## Contradictory results @@ -315,8 +316,8 @@ primal_feasibility_report(model, Dict(x => 0.0, y => -1e-8)) # `(x, y) = (-1, 0)` and the second is feasible `(x, y) = (0, -1e-8)`. Different # algorithms may terminate at either of these bases. -# Another example is a variation on our integrality eample, but this time, there -# is are constraint that `x >= 1` and `y <= 0.5`: +# Another example is a variation on our integrality example, but this time, there +# are constraints that `x >= 1` and `y <= 0.5`: M = 1e6 model = Model(HiGHS.Optimizer)