Objective Sensitivity 2.0 #303
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….jl into ar/dualparameter
* fix conic error * use jump psd problem * [docs] update to Documenter@1 (#286) * [docs] update to Documenter@1 * Update * update * format * Pass attributes through Objective.FunctionConversionBridge (#287) * Pass attributes through Objective.FunctionConversionBridge * Fix * add test * fix tol * fix test * add reverse test --------- Co-authored-by: joaquimg <[email protected]> * bump POI * cleanup --------- Co-authored-by: Oscar Dowson <[email protected]> Co-authored-by: Benoît Legat <[email protected]> Co-authored-by: joaquimg <[email protected]>
* prepare more tests * sketch * temp examples * remove printing * remove printing * remove duplicatie def * move definition * format * format * simplify conic model * force nlp on nlp tests * fix param tests * cleanup parameter usage * remove code * cleanup usage of parameters * format * add temp dep * format * add temp dep * fix PSDSquare * temp fix for tests * format
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docs/src/usage.md
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| Using Lagrangian duality we could already calculate the objective sensitivity with respect to parameters that appear in the RHS of the constraints (e.g, `cons` in this case for parameter `p`) - i.e. The objective sensitivity w.r.t. a parameter change in the RHS of the constraints is given by the optimal multiplier. | ||
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| On the other hand, if the parameter appears in the LHS of the constraints, we can calculate the objective sensitivity with respect to the parameter using: the sensitivities of the variables with respect to the parameter, \( \frac{\partial x}{\partial p} \), and the gradient of the objective with respect to the variables \( \frac{\partial f}{\partial x} \): |
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So this means you can compute it using the dual objective if you only have parameters as constraint constants and you can also use it with the primal objective using the solution sensitivity which also works even if you have parameters as constraint coefficients.
2 questions the readers might have:
- If you only have parameters on the constraint constants, would computing the sensitivity using the primal or dual objective match ?
- Why not use the dual objective but also include the sensitivity of the dual solution ?
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Probably it would make sense to also add ForwardDualObjectiveSensitivity (in another PR of course) ?
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This is a good point. I will add an issue for this.
My naive response for now is:
If you only have parameters on the constraint constants, would computing the sensitivity using the primal or dual objective match?
Yes, and we add this as a test. Also added a sentence on this:
Line 155 in 43d6eb8
Why not use the dual objective but also include the sensitivity of the dual solution?
Added a sentence on this (and equivalence under strong duality) and will create an issue
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Sentence:
Lines 189 to 194 in f8042b9
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Issue #315
Had issues with my old pr (#282). So this one is the updated version.