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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
Accepted
Minimizing a sum of functions
Unless your functions have a very special structure (convex? independent as in @Gerhard's comment? smooth?) I (a) don't see how you can differentiate [you say your functions are piecewise], and (b) do …
- 96.4k
0
votes
Lagrangian duality
Unless I am confused, this is proved in Boyd-Vanderberghe "Convex Optimization", page 244.
- 96.4k
1
vote
LP/QP with not-so-constant linear constaints
You may want to consult the oevre of Spielman and Teng (I think all their papers are on ArXiv). They study this sort of question in great depth.
- 96.4k
0
votes
relation between solution of a linear program and its perturbation
The magic words are Spielman and Teng.
- 96.4k
3
votes
Accepted
finding an element of a vector subspace contained in the first orthant
@Ben's answer is within $\epsilon$ of correct. The problem with it is that (depending on how you interpret the constrains $x_i \geq 1$) there might be no solution with either a specific $x_{i_0} > 0,$ …
- 96.4k
1
vote
Convex optimization over vector space of varying dimension
Dimension minimization problems are notoriously hard (a standard example is: given a graph $G,$ what is the minimal dimension Euclidean space where the graph can be embedded with unit edge lengths? (m …
- 96.4k
1
vote
Sparse Principal Components Analysis: Any practical examples with fixed rank correlation mat...
Most examples of principal component analysis are of the type you describe (since people usually want to know the (eg) top three principal components). Look at SVDPACK or PROPACK.
Edit It is true tha …
- 96.4k
15
votes
When does symmetry in an optimization problem imply that all variables are equal at optimality?
The most common condition for symmetry in my experience is convexity: if the feasible region is symmetric and convex, and the objective function is convex, it is immediate that argmin has all variable …
- 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
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
2
votes
Optimal tax Rate
A response to the OP's comment than to the original question. The income distribution is definitely NOT gaussian -- a lot of thought has been devoted to figuring out what exactly it is, which thought …
- 96.4k
3
votes
Is a solution of a linear system of semidefinite matrices a convex combination of rank 1 sol...
The answer seems obviously "no", since a system of equations need not have any rank one solutions (for example, the solution set can be the line $x I_n,$ where $I_n$ is the identity matrix.)
- 96.4k
4
votes
Maximizing positive definite quadratic using the eigendecompoisition
The reference where all is revealed is Bodlaender, Gritzman, Klee, Van Leeuwen
- 96.4k
4
votes
Mean curvature of polyhedral surfaces
I am a little puzzled by the Polthier reference, since at least one definition of PL mean curvature goes back to at least T. Regge's classic paper
MR0127372 (23 #B418)
Regge, T.
General relativity w …
- 96.4k