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Add duality-gap thresholds #169

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merged 17 commits into from Jan 17, 2023

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stephane-caron
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Working draft accompanying the discussion in #168

Closes #168

@hrp2-14
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hrp2-14 commented Jan 16, 2023

Hi ! This project doesn't usually accept pull requests on the main branch.
If this wasn't intentionnal, you can change the base branch of this PR to devel
(No need to close it for that). Best, a bot.

@jcarpent jcarpent changed the base branch from main to devel January 16, 2023 10:50
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Thanks @stephane-caron for the PR.
I would just recommend changing the choice of variable naming to use the full name duality_gap for clarity and transparency.

bindings/python/src/expose-settings.hpp Outdated Show resolved Hide resolved
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stephane-caron commented Jan 16, 2023

Ready for review! The main difference since last review is the proposal to replace the instructions:

-  duality_gap /= sqrt_max_dim; // in order to get an a-dimensional duality gap
-  rhs_duality_gap /= sqrt_max_dim;

By a recommendation in the docs:

... contrary to residuals which result from an infinite norm, the duality gap scales with the square root of the problem dimension (thus it is numerically harder to achieve a given duality gap for larger problems). A recommended choice is $\epsilon^{\text{gap}}_{\text{abs}} = \epsilon_{\text{abs}} \sqrt{\max(n, n_{\text{eq}}, n_{\text{ineq}})}$.

The rationale for it is that the new parameters allow users to decide by themselves how they want to handle the duality gap.

@stephane-caron stephane-caron marked this pull request as ready for review January 16, 2023 13:14
@jcarpent jcarpent merged commit 3d2001b into Simple-Robotics:devel Jan 17, 2023
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Absolute duality gap stopping criterion
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