Update: improve performance simplexDual#1125
Merged
Merged
Conversation
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
This change simplifies
simplexDualby replacing the previous enlarged LP formulation with a shifted-variable formulation. Previously, the max-min problem was expressed by introducing explicit inequality constraints,which required constructing an additional inequality matrix using
eye(n)and solving the expanded LP.The new formulation writes
where$z \ge 0$ and $t \ge 0$ are handled directly by the simplex formulation. Substituting into the equality constraint gives
with objective
implemented as
This reduces the LP size, avoids constructing the explicit inequality matrix, and solves the problem directly using
simplex.The output contract remains unchanged:
and
Additional cleanup includes normalizing
bas a column vector and clamping the recoveredx_minto zero to avoid small negative numerical artifacts.