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visits member for 3 years, 4 months
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Apr
13
comment Solving a non-convex quadratically constrained quadratic program
there are also moment matrices approaches due to J.Lasserre et al. Tools like YALMIP users.isy.liu.se/johanl/yalmip implement parts of this.
Apr
13
comment Solving a non-convex quadratically constrained quadratic program
What you wrote in the comment above: "find the smallest sphere touching the intersection of some ellipsoids" is a not a description of the problem in your question. The latter is not convex, the former is. Which of the two are you trying to solve?
Apr
12
comment Solving a non-convex quadratically constrained quadratic program
Intersection of ellipsoids is convex. What exactly do you mean by "the smallest sphere"? Do you mean to look for a point of minimal norm in the intersection? If yes, this is a convex problem, and your formulation has a bug, it appears...
Apr
12
answered Solving a non-convex quadratically constrained quadratic program
Apr
12
revised do you know this determinant (basic commutative algebra)?
fixed one more typo
Apr
12
comment do you know this determinant (basic commutative algebra)?
Thank you. We totally overlooked this...
Apr
12
accepted do you know this determinant (basic commutative algebra)?
Apr
11
comment do you know this determinant (basic commutative algebra)?
@David: it's my typo, I fixed it now; it should be $|J|=n-d$, not $d$. Thanks for spotting it!
Apr
11
revised do you know this determinant (basic commutative algebra)?
corrected a typo: $|J|=n-d$, not $d$
Apr
11
asked do you know this determinant (basic commutative algebra)?
Apr
6
comment Is that true all the convex optimization problems can be solved in polynomial time using interior-point algorithms
@Suvrit: right. There is a theorem about "equivalence of separation and optimization" for convex problems, i.e. you can solve convex problems in polynomially many (in the dimension, and diameter of the feasible set) calls to the separation oracle.
Apr
4
comment Working with group cosets in MAGMA
gap-system.org/Doc/Learning/learning.html contains quite a few links to tutorials, examples, etc. gap-system.org/Doc/forumarchive.html (GAP Forum) is a mailing list you can subscribe to.
Apr
3
comment Efficient topological triangulations of non-convex polyhedra
Thanks. I'd appreciate a standard reference to these definitions, as I tried to locate one, unsuccessfully.
Apr
3
comment Working with group cosets in MAGMA
IMHO, GAP language is easier to use, in particular it's much less strict in the ways it handles types of data. And you can read (and modify, if needed) the GAP source code if you're really stuck :-)
Apr
3
comment Families of three dimensional algebraic curves
Do you mean "algebraic curve defined by sparse equations"?
Apr
3
awarded  Nice Answer
Apr
3
comment Efficient topological triangulations of non-convex polyhedra
It seems that the definition of polyhedron you use differs from the one used by Chazelle in your reference to "a classical construction". Would you mind to give a definition? In my "book", a (nonconvex) polyhedron is a union of finitely many convex polyhedra. Chazelle talks about the boundary of such an object.
Apr
3
comment Is that true all the convex optimization problems can be solved in polynomial time using interior-point algorithms
even SDPs, however, cannot be solved in polynomial time, or at least no algorithms like this are known. See my answer below.
Apr
3
comment Is that true all the convex optimization problems can be solved in polynomial time using interior-point algorithms
However, there are NP-hard convex optimization problems. (see my answer below)
Apr
3
answered Is that true all the convex optimization problems can be solved in polynomial time using interior-point algorithms