A primal--dual interior-point method for nonsymmetric conic optimization with conjugate-free scaling

What the math gives to ML

The transferable asset is not the conic formulation itself, but the use of a single-secant BFGS metric as a conjugate-free substitute for an unavailable curvature object, together with safeguards that keep the approximate metric uniformly comparable to the true barrier Hessian. This suggests a neural optimizer that builds a cheap blockwise curvature preconditioner from one recent parameter-gradient secant, while clipping its spectrum relative to an RMS/diagonal baseline. The paper's predictor-corrector and homogeneous self-dual machinery is less directly applicable, but the metric-comparability principle provides a concrete stability criterion for adaptive second-order updates.