Improve max ball computation and develop analytic center computation #310
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June 18, 2024 14:23
…_internal_point_computations
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June 20, 2024 12:25
vfisikop
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Jun 21, 2024
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| Output: (i) The analytic center of the polytope | ||
| (ii) A boolean variable that declares convergence | ||
| */ |
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A reference for the algorithm / definitions would be useful here.
e.g. Convex Optimization, Boyd and Vandenberghe (Sect. 8.5.3)
| d.noalias() = - H.lu().solve(grad); | ||
| Ad.noalias() = A * d; | ||
| // Compute the step length | ||
| step = std::min(NT(0.99) * get_max_step<VT, NT>(Ad, b_Ax), NT(1)); |
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The step should always equal to 1, the NT(0.99) * get_max_step<VT, NT>(Ad, b_Ax) is useful to deal with very hard skinny cases where the analytic center is near to the boundary and to avoid numerical overflows when computing the gradient and the Hessian. I'm using the same epsilon as in the analytic center computation in crhmc preprocessing. I changed the 0.99 to NT(1) - tol_bnd while const NT tol_bnd = NT(0.01);.
| { | ||
| const int m = Ad.size(); | ||
| NT max_element = std::numeric_limits<NT>::lowest(), max_element_temp; | ||
| for (int i = 0; i < m; i++) { |
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I think we mostly use the style
for
{
....
}
in the library, would you mind switch to that style?
| do { | ||
| iter++; | ||
| // Compute the direction | ||
| d.noalias() = - H.lu().solve(grad); |
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If I understand correctly the Hessian is psd so you can use Cholesky here, right?
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Thanks. Yes, exactly, done
TolisChal
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…310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments --------- Authored-by: Apostolos Chalkis (TolisChal) <tolis.chal@gmail.com>
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…310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
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…eomScale#310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
TolisChal
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Jul 7, 2024
…eomScale#310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
TolisChal
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Jul 8, 2024
…eomScale#310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
TolisChal
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Jul 8, 2024
…eomScale#310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
TolisChal
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to TolisChal/volume_approximation
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Jul 8, 2024
…eomScale#310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
TolisChal
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Jul 17, 2024
…310) * improve the implementation of maximum ellipsoid computation * minor fix in rounding unit-test * fix file copyrights * fix max_ball bug and create new unit test * fix max_ball bug and create new unit test * apply termination criterion after transformation in max ellipsoid rounding * imrpove skinny poly generator's interface * improve stopping criterion and seed setting * complete unit tests implementations * implement Newton method to compute the analytic center * minor changes * resolve PR comments * complete analytic center computation * resolve conflicts * minor changes * minor changes * minor changes * improve new unit tests * resolve PR comments
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