Opened 9 months ago
Last modified 3 months ago
#31376 new enhancement
Complex of differentiable manifolds associated with active sets of nonlinear optimization problems
Reported by: | mkoeppe | Owned by: | |
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Priority: | major | Milestone: | sage-9.5 |
Component: | manifolds | Keywords: | |
Cc: | yzh | Merged in: | |
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Just like a polytope can be written as the finite disjoint union of relative interiors of its faces, we can write the feasible set of (well-behaved...) nonlinear optimization problems as the finite disjoint union of differentiable manifolds of different dimensions. Their closures are manifolds with corners (#30080...), which together form a CW complex.
In the special case of the simplex method for LP in standard equation form:
- a basic solution is a submanifold of dimension 0 embedding into the affine space defined by the equations
- the nonbasic variables form an adapted chart of that space.
In the more general case of convex quadratic programming:
- an active set determines a submanifold (an affine subspace) of some dimension
Change History (3)
comment:1 Changed 7 months ago by
- Milestone changed from sage-9.3 to sage-9.4
comment:2 Changed 6 months ago by
- Cc yzh added
- Description modified (diff)
comment:3 Changed 3 months ago by
- Milestone changed from sage-9.4 to sage-9.5
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