Monday, 14 February
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Morning session (9h00 - 12h30):
Optimization on manifolds: introduction and motivating examples
(eigenvalue problem, independent component analysis, constrained linear regression, low-rank optimization). - R. Sepulchre
Manifolds, submanifolds, quotient manifolds; Lie groups and homogeneous spaces. - P.-A. Absil
Afternoon session (14h - 17h30):
First-order geometry: Tangent vectors, Riemannian metric, gradient vector fields, gradient
flows. - R. Sepulchre
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Tuesday, 15 February
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Morning session (9h00 - 12h30):
First-order algorithms: Retractions, seepest-descent methods,
line-search strategies. Optimization on the orthogonal group and
independent component analysis. - P.-A. Absil
Afternoon session (14h - 17h30):
Free
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Wednesday, 16 February
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Morning session (9h00 - 12h30):
Second-order geometry and Newton's method: Newton's method in Rn , affine connections,
Riemannian connection, parallel translation, geodesics, Newton's
method on manifolds. - R. Sepulchre
Afternoon session (14h - 17h30):
Models and trust-region methods. Optimization of the Rayleigh quotient on the sphere and
on the Grassmann manifold. - P.-A. Absil
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Thursday, 17 February
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Morning session (9h00 - 12h30):
Vector transport, approximate Newton methods, conjugate
gradients. Applications. - P.-A. Absil
Afternoon session (14h - 17h30):
The geometry of optimization algorithms with rank constraints. - R. Sepulchre
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