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Hello all, I want to submit to you an idea about quasi-Newton operators.
Currently, we have LBFGSOperator to build a convex quasi-Newton approximation and LSR1Operator to catch negative curvatures.
I wonder if we can build a limited-memory operator that could use both BFGS and SR1 equations.
Even if positive definitness is lost, we get more chance to satisfy numerical safeguards.
Contrary to a damped operator, it keeps the real curvature instead of a damped one.
where $B_k$ may be initially set as a multiple of the identity.
This QNOperator could choose automatically which update perform based on the satisfaction of numerical safeguards.
It would keep the related vectors and adapt product accordingly to the update selected.
What do you think?
The text was updated successfully, but these errors were encountered:
Hello all, I want to submit to you an idea about quasi-Newton operators.
Currently, we have LBFGSOperator to build a convex quasi-Newton approximation and LSR1Operator to catch negative curvatures.
I wonder if we can build a limited-memory operator that could use both BFGS and SR1 equations.
Even if positive definitness is lost, we get more chance to satisfy numerical safeguards.
Contrary to a damped operator, it keeps the real curvature instead of a damped one.
Suppose a first LBFGS update
and then, a LSR1 update
with$r_{k+1} = y_k{k+1} - B_{k+1} s_{k+1}$ .$B_{k+2} v$ as
Then we get the product
where$B_k$ may be initially set as a multiple of the identity.
This QNOperator could choose automatically which update perform based on the satisfaction of numerical safeguards.
It would keep the related vectors and adapt product accordingly to the update selected.
What do you think?
The text was updated successfully, but these errors were encountered: