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Results tagged with oc.optimization-and-control
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user 11142
Operations research, linear programming, control theory, systems theory, optimal control, game theory
1
vote
Embedding a graph in $\mathbb{R}^3$ with partial geometric information
There are a number of papers by Mike Treacy (I. Rivin is a co-author on some) which address this problem, but in a purely practical manner, using essentially the scheme proposed by Bullet51. Here is o …
- 96.4k
4
votes
Nearest matrix orthogonally similar to a given matrix
Depends what you mean by "technique". Your problem is a quadratically constrained quadratic program. To be precise, the objective function is
$$\mbox{tr} (A-TBT^t)(A^t - TB^t T^t) = \mbox{tr} ( AA^t …
- 96.4k
2
votes
Accepted
Distribution of eigenvectors and eigenvalues for random, symmetric matrix
It sounds like the OP has a random perturbation of a fixed graph, which is not considered very frequently, but when they have, it seems to be by A. Flaxman (see, e.g.:
Expansion and lack thereof in r …
- 96.4k
0
votes
Optimization problem with determinant as objective
Your constraints are linear on the entries of $S,$ since in your case the singular values are equal to the eigenvalues (since $S$ is symmetric positive definite) and so their sum is the trace. I assum …
- 96.4k
1
vote
Accepted
Efficient algorithm for Wasserstein-1 distance in graph setting
See this PLOS paper for algorithm and extensive survey. (Gottschlich and Schumacher, 2014)
- 96.4k
1
vote
Efficient algorithm for Wasserstein-1 distance in graph setting
I could be wrong, but this seems to be addressed in this 2013 paper.
- 96.4k
3
votes
Accepted
Do computational geometers use Lagrange multipliers?
A convex optimization method for constructing a set of points in the plane with prescribed (combinatorial) Delaunay triangulation is given in
Euclidean structures on simplicial surfaces and hyperbol …
- 96.4k
1
vote
Accepted
Functions that are easy to compare to a norm
If $f$ is homogeneous, you can just try to minimize it on the unit ball (which is a Lagrange multiplier problem, which does not mean it's easy), and see if any of your critical values are smaller than …
- 96.4k
6
votes
The Maximal $\ell_2$ norm of a signed sum of vectors
This is, in essence, the most general form of the zero-one quadratic programming problem, and is known to be NP-complete. (see, for example, Computational Aspects of a Branch and Bound Algorithm for
Q …
- 96.4k
1
vote
The distribution of the shortest path through $n$ points
It seems that even the constant in front of the $\sqrt{n}$ is not known, but there are experimental results which seem to describe the distribution pretty well. In particular, it seems that the varian …
- 96.4k
1
vote
Finding the maximum of a multivariate polynomial of degree one
You are trying to maximize a convex function over a convex set (in your case a slice of a high-dimensional cube. This has been studied a lot, and you can see this stackexchange discussion for referenc …
- 96.4k
2
votes
Explicit formula for an LMI solution
I would say that the answer is NO, since your problem is basically the general semidefinite program. There are obviously tractable special cases (like, if $A_1$ is psd, then you can set $x_i = \delta_ …
- 96.4k
3
votes
A nice necessary and sufficient condition on positive semi-definiteness of a matrix with a s...
I very much doubt that a necessary and sufficient condition exists. For example, for finite element approximations to the Laplacian in a planar domain, you will get the (potentially non-zero) off-diag …
- 96.4k
2
votes
Is unconstrained integer convex optimization problem NP-hard?
Yes, since the shortest vector in lattice problem is NP-hard, see http://en.wikipedia.org/wiki/Lattice_problem
- 96.4k
0
votes
relation between solution of a linear program and its perturbation
The magic words are Spielman and Teng.
- 96.4k