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Based on revising some modified BFGS update formulae, we construct some new quadratic approximation models to develop several approximate optimal stepsizes.
Two approximating functions are tested here, one employing quadratic approximation of the hydraulic head (flux is linear), the other cubic approximation.
The key idea is to use the criterion of DQ-optimality, which is a quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix.
Hsieh, C.-J., Sustik, M. A., Dhillon, I. S. & Ravikumar, P. Quic: quadratic approximation for sparse inverse covariance estimation.
Design principle 2: Optimize hyperparameters at each step to minimize a local quadratic approximation.
The update uses a quadratic approximation of the arrival cost and information about the previously active or inactive constraints.
Most methods rely on repeatedly solving a quadratic approximation of the NLP.
A second order method is a Newton or quasi-Newton method, employing a local quadratic approximation.
This paper proposes DOPUS, a novel update scheme for the quadratic approximation of the NLP.
The NPV functional is efficiently maximized using a Bound Optimization BY Quadratic Approximation, BOBYQA, algorithm.
On a quadratic approximation, this guarantees convergence of all model variables at a common rate, though it empirically extends to certain non-convex objectives.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com