#16714: Add a matrix of constraints in a LP
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Reporter: ncohen | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.3
Component: linear | Resolution:
programming | Merged in:
Keywords: | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | 846cba629c68e46f274de8d6cbbaabd3cdbb0a99
u/vbraun/add_a_matrix_of_constraints_in_a_lp| Stopgaps:
Dependencies: |
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Comment (by dimpase):
Replying to [comment:8 vbraun]:
> I've started with tensors (over the base ring) of linear functions and
free modules. This implements:
> {{{
> ...
> sage: v * m # MIPVariable * matrix
> (3.0, 4.0)*x_1 + (1.0, 2.0)*x_0
> }}}
this is very nice; I hope this can be a basis for implementing an
interface to "conic programming". That is, whenever you have a convex cone
K in `R^n` (e.g. the positive ortant, or `{(x_0,...,x_{n-1}) | x_0^2 >=
sum_{j=1}^{n-1} x_j^2}`, known as "icecream cone") you have a partial
order `<_K` on `R^n` defined by `x<_K y` iff y-k is in K.
then one can do linear optimisation on the intersection of K with an
affine subspace. For K being the positive ortant this is just the usual
LP; for K the icecream cone this is a kind of norm minimisation, etc.
CVXOPT has implementations for several different cones like this (by the
way, semidefinite programming is yet another example, K being the cone of
psd matrices in `R^nxn`).
--
Ticket URL: <http://trac.sagemath.org/ticket/16714#comment:12>
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