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SUMMARY:Infeasible Optimization on Manifolds: the Landing Approach - Pierr
 e-Antoine Absil (University of Louvain)
DTSTART:20251030T150000Z
DTEND:20251030T160000Z
UID:TALK239266@talks.cam.ac.uk
CONTACT:Georg Maierhofer
DESCRIPTION:Classic first-order optimization methods on a submanifold of a
  Euclidean space are based on two ingredients: (i) choosing a search direc
 tion at the current iterate and (ii) applying a retraction to produce poin
 ts along a manifold-valued curve tangent to the search direction. It is no
 w well established that ingredient (ii) can be computationally considerabl
 y more costly than ingredient (i) even for well-known manifolds such as th
 e Stiefel manifold\, notably in a stochastic gradient context where (i) ca
 n be particularly cheap. This has prompted the development of infeasible o
 ptimization methods that do not enforce the manifold constraint at the ite
 rates but still exploit the manifold nature of the feasible set. The landi
 ng approach\, which is the topic of this talk\, belongs to this recent tre
 nd. It performs an update along a weighted sum of two terms. One term\, ta
 ngent to the active "layered manifold"\, decreases the objective function 
 while preserving the constraint function at the first order. The other ter
 m decreases infeasibility. Under mild assumptions and with sufficiently sm
 all step size\, the method provably converges to critical points. Moreover
 \, in the stochastic case where the update vector is affected by additive 
 zero-mean bounded-variance noise\, the landing algorithm with suitably dim
 inishing step size is proved to converge in expectation. This talk is base
 d on joint work with Pierre Ablin\, Bin Gao and Simon Vary (arXiv:2303.165
 10\, arXiv:2405.01702).
LOCATION:Centre for Mathematical Sciences\, MR14
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