More flexible regularization of Newton step#44
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…cluding lagrangian hessian regularization for games
lassepe
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Aug 15, 2025
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LGTM modulo minor comments
| mcp.∇F_z!(∇F, x, y, s; θ, ϵ) | ||
| end | ||
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| if regularize_linear_solve === :identity |
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This could be folded into a elseif of above
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I considered that, but thought the logic was simpler this way. Basically, for :internal mode you need to regularize ∇F directly when computed in place, and for both :identity and :none you compute it without the extra parameter. Then, for :identity only do you modify it when passing to the linear solver by adding an explicit scaled identity (if ∇F is square).
src/mcp.jl
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| """ | ||
| struct PrimalDualMCP{T1,T2,T3} | ||
| "A callable `F!(result, x, y, s; θ, ϵ)` which computes the KKT error in-place." | ||
| "A callable `F!(result, x, y, s; θ, ϵ, [η])` to the KKT error in-place." |
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| "A callable `F!(result, x, y, s; θ, ϵ, [η])` to the KKT error in-place." | |
| "A callable `F!(result, x, y, s; θ, ϵ, [η])` to compute the KKT error in-place." |
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Adds an additional kwarg in the solver which allows the user to specify how the Newton step computation should be regularized. Currently supports three options:
:none(no regularization):identity(adds scaled identity to the KKT Jacobian):internal(assumes that the Symbolics-generated KKT Jacobian accepts a regularization parameter directly)Also adds an example of
:internalregularization ingame.jlwhere we add a scaled identity only to the blocks of the KKT Jacobian that correspond to the Hessian of each player's Lagrangian wrt its decision variable.Also adds some minimal logic to adjust regularization strength depending upon success/failure of inner loop solves.