Tuesday, 15:45 - 16:10 h, Room: H 3503

 

Afonso Bandeira
On sparse Hessian recovery and trust-region methods based on probabilistic models

Coauthors: Katya Scheinberg, Luís Nunes Vicente

 

Abstract:
In many application problems in optimization, one has little or no
correlation between problem variables, and such (sparsity) structure
is unknown in advance when optimizing without derivatives.
We will show that quadratic interpolation models computed by
l1-minimization recover the Hessian sparsity of the function
being modeled, when using random sample sets. Given a considerable
level of sparsity in the unknown Hessian of the function,
such models can achieve the accuracy of second order Taylor ones
with a number of sample points (or observations) significantly
lower than O(n2).
The use of such modeling techniques in derivative-free optimization
led us to the consideration of trust-region methods where the
accuracy of the models is given with some positive
probability. We will show that as long as such probability of
model accuracy is over 1/2, one can ensure, almost surely,
some form of convergence to first and second order stationary points.

 

Talk 2 of the invited session Tue.3.H 3503
"Novel approaches in derivative-free optimization" [...]
Cluster 6
"Derivative-free & simulation-based optimization" [...]

 

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