MATH-512 Optimization on manifolds

MATH-512 Optimization on manifolds

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We develop, analyze and implement numerical algorithms to solve optimization problems of the form: min f(x) where x is a point on a smooth manifold. To this end, we first study differential and Riemannian geometry (with a focus dictated by pragmatic concerns). We also discuss several applications.

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701 - Geodesic convexity: why, and what we need 1 of 15

duration 9 minutes 49 seconds

701 - Geodesic convexity: why, and what we need

701 - Geodesic convexity: why, and what we need

701 - Geodesic convexity: why, and what we need

701 - Geodesic convexity: why, and what we need

From Nicolas Boumal

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112.2 - Comparing tangent vectors: parallel… 2 of 15

duration 6 minutes 41 seconds

112.2 - Comparing tangent vectors: parallel…

112.2 - Comparing tangent vectors: parallel transport - Toward a definition

112.2 - Comparing tangent vectors: parallel…

112.2 - Comparing tangent vectors: parallel transport - Toward a definition

From Nicolas Boumal

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702.2 - Geodesic convexity - Basic facts and more… 3 of 15

duration 15 minutes 59 seconds

702.2 - Geodesic convexity - Basic facts and more…

702.2 - Geodesic convexity - Basic facts and more definitions

702.2 - Geodesic convexity - Basic facts and more…

702.2 - Geodesic convexity - Basic facts and more definitions

From Nicolas Boumal

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702.1 - Geodesic convexity - Basic definitions 4 of 15

duration 14 minutes 50 seconds

702.1 - Geodesic convexity - Basic definitions

702.1 - Geodesic convexity - Basic definitions

702.1 - Geodesic convexity - Basic definitions

702.1 - Geodesic convexity - Basic definitions

From Nicolas Boumal

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503.3 - Tangent vectors without embedding space -… 5 of 15

duration 18 minutes 36 seconds

503.3 - Tangent vectors without embedding space -…

503.3 - Tangent vectors without embedding space - Making tangent spaces linear

503.3 - Tangent vectors without embedding space -…

503.3 - Tangent vectors without embedding space - Making tangent spaces linear

From Nicolas Boumal

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503.2 - Tangent vectors without embedding space -… 6 of 15

duration 12 minutes 44 seconds

503.2 - Tangent vectors without embedding space -…

503.2 - Tangent vectors without embedding space - Tangent vectors as equivalence classes

503.2 - Tangent vectors without embedding space -…

503.2 - Tangent vectors without embedding space - Tangent vectors as equivalence classes

From Nicolas Boumal

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503.1 - Tangent vectors without embedding space -… 7 of 15

duration 10 minutes 4 seconds

503.1 - Tangent vectors without embedding space -…

503.1 - Tangent vectors without embedding space - Revisiting the embedded case

503.1 - Tangent vectors without embedding space -…

503.1 - Tangent vectors without embedding space - Revisiting the embedded case

From Nicolas Boumal

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502.3 - Smooth sets and functions - Smooth… 8 of 15

duration 21 minutes 2 seconds

502.3 - Smooth sets and functions - Smooth…

502.3 - Smooth sets and functions - Smooth functions, topology, and manifolds

502.3 - Smooth sets and functions - Smooth…

502.3 - Smooth sets and functions - Smooth functions, topology, and manifolds

From Nicolas Boumal

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502.2 - Smooth sets and functions - Example:… 9 of 15

duration 8 minutes 22 seconds

502.2 - Smooth sets and functions - Example:…

502.2 - Smooth sets and functions - Example: atlas for a circle

502.2 - Smooth sets and functions - Example:…

502.2 - Smooth sets and functions - Example: atlas for a circle

From Nicolas Boumal

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502.1 - Smooth sets and functions - Charts and… 10 of 15

duration 22 minutes 19 seconds

502.1 - Smooth sets and functions - Charts and…

502.1 - Smooth sets and functions - Charts and atlases

502.1 - Smooth sets and functions - Charts and…

502.1 - Smooth sets and functions - Charts and atlases

From Nicolas Boumal

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501.2 - From embedded to general manifolds - How,… 11 of 15

duration 12 minutes 8 seconds

501.2 - From embedded to general manifolds - How,…

501.2 - From embedded to general manifolds - How, and why again

501.2 - From embedded to general manifolds - How,…

501.2 - From embedded to general manifolds - How, and why again

From Nicolas Boumal

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501.1 - From embedded to general manifolds - Why? 12 of 15

duration 7 minutes 39 seconds

501.1 - From embedded to general manifolds - Why?

501.1 - From embedded to general manifolds - Why?

501.1 - From embedded to general manifolds - Why?

501.1 - From embedded to general manifolds - Why?

From Nicolas Boumal

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213.2 - Linear convergence with… 13 of 15

duration 19 minutes 38 seconds

213.2 - Linear convergence with…

213.2 - Linear convergence with Polyak-Łojasiewicz - Strong g-convexity implies PŁ

213.2 - Linear convergence with…

213.2 - Linear convergence with Polyak-Łojasiewicz - Strong g-convexity implies PŁ

From Nicolas Boumal

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213.1 - Linear convergence with… 14 of 15

duration 8 minutes 48 seconds

213.1 - Linear convergence with…

213.1 - Linear convergence with Polyak-Łojasiewicz - Mechanical proof

213.1 - Linear convergence with…

213.1 - Linear convergence with Polyak-Łojasiewicz - Mechanical proof

From Nicolas Boumal

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114.2 - Distance, geodesics and complete… 15 of 15

duration 9 minutes 11 seconds

114.2 - Distance, geodesics and complete…

114.2 - Distance, geodesics and complete manifolds - Complete manifolds

114.2 - Distance, geodesics and complete…

114.2 - Distance, geodesics and complete manifolds - Complete manifolds

From Nicolas Boumal

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Managers:: Nicolas Boumal
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Appears In:: EPFL courses