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Results tagged with convex-optimization
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user 11142
Optimization with convex constraints and convex objectives; notions related to convex optimization such as sub-gradients, normal cones, separating hyperplanes
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Optimization of non-smooth convex function in a polytope
A good survey may be found here: www.mat.univie.ac.at/~herman/skripten/NCO_OSGA.pdf
(M Ahookosh, 2017)
- 96.4k
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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
2
votes
Algorithm for a linear optimization problem
I am not sure I understand the question. The constraints are a system of linear equations and inequalties in the variables $p_{ij}$ and the objective function is linear. So, this is a box generic line …
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Has anyone developed a technique to generate a polytope given (possibly redundant) inequalit...
The magic words are "Motzkin's double description method"
- 96.4k
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Accepted
Find the minimum distance between two convex hulls
This is discussed at length here. (Kaown and Liu, 2009)
- 96.4k
3
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How to prove the existence of the polytope in $\mathbb{R}^d$ with a given number of faces, m...
This is an explanation of Anton's comment. For each set of $f$ unit vectors, one finds the polytope minimizing the isoperimetric quotient. The set of configurations of $f$ (not necessarily distinct) u …
- 96.4k
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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
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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
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Distance between two sets
There is a much earlier (and seemingly very efficient) algorithm by Gilbert, Johnson, Kerthi. (1988, IEEE Journal of Robotics and Automation).
- 96.4k
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Lagrange multiplier and semidefinite programming
For all you ever wanted to know about this, check out Boyd and Vanderberghe's Convex Optimization, especially the part on KKT. In fact, that page advertises a MOOC on Convex Optimization...
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maximizing convex quadratic form over the intersection of unit sphere and positive orthant
The magic words are quadratically constrained quadratic programming. And semidefinite programming.
EDIT I misread the question (it is a convex maximization problem). This is still somewhat tractable …
- 96.4k
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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
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How to Find a Matrix Closest to a Given One Under Certain Constraints
This seems to be covered by the wikipedia.
- 96.4k
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Can all convex optimization problems be solved in polynomial time using interior-point algor...
You should check out Boyd-Vanderberghe's convex optimization, available for free on Boyd's web page at Stanford. This has a discussion of the "easy" classes of convex optimization problems (google "se …
- 96.4k
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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 …
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