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Abstract
A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with
disjoint linear constraints is presented. In the considered class of
problems, a subset of variables are subject to linear equality constraints,
while variables in a different subset are constrained to remain in a convex set.
The proposed algorithm exploits the structure by combining steps in the
nullspace of the equality constraint's matrix with projections onto the convex set. The algorithm is motivated by application in weather forecasting.
Numerical results on a simple model designed for predicting rain show that the
algorithm is an improvement on current practice and that it reduces the
computational burden compared to a more general interior point QO method.
In particular, if constraints are disjoint and the rank of the set of linear
equality constraints is small, further reduction in computational costs can be
achieved, making it possible to apply this algorithm in high dimensional
weather forecasting problems.
disjoint linear constraints is presented. In the considered class of
problems, a subset of variables are subject to linear equality constraints,
while variables in a different subset are constrained to remain in a convex set.
The proposed algorithm exploits the structure by combining steps in the
nullspace of the equality constraint's matrix with projections onto the convex set. The algorithm is motivated by application in weather forecasting.
Numerical results on a simple model designed for predicting rain show that the
algorithm is an improvement on current practice and that it reduces the
computational burden compared to a more general interior point QO method.
In particular, if constraints are disjoint and the rank of the set of linear
equality constraints is small, further reduction in computational costs can be
achieved, making it possible to apply this algorithm in high dimensional
weather forecasting problems.
Original language  English 

Publisher  Arxiv 
Volume  1909.04991 
Publication status  Published  12 Sep 2019 
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Projects
 1 Active

Recent developments in optimization methods for data assimilation in oceanography
SARTENAER, A., LALOYAUX, P., TOINT, P., Tshimanga Ilunga, J. & Gürol, S.
1/09/07 → …
Project: PHD
Activities

Parallelizing Weak Constraint 4DVAR?
Philippe Toint (Speaker)
5 Oct 2016Activity: Talk or presentation types › Invited talk

Oberwolfach Worksuop on Data Assimilation 2016
Philippe Toint (Contributor)
2 Oct 2016 → 8 Oct 2016Activity: Participating in or organising an event types › Participation in conference