All Questions
984 questions
1
vote
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185
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Compute generalized pentagram map
Hi,
(This is my first question on MathOverflow! :-)
Imagine you have a set of points $S = \{p_1, \ldots, p_n\}$ in $\mathbb{R}^d$, of which $t$ are "bad". I want to compute a "safe convex hull", ...
- 11
0
votes
0
answers
194
views
A linear program related question
Dear all, recently, I encountered the following problem. It is closely related to the order of growth for UMD constants of all $n$-dimensional Banach lattice.
Let $\alpha^k \in (\alpha_1^k, \alpha_2^...
- 769
1
vote
0
answers
75
views
Are there any known bounds on the value of solutions of linear integer programming?
Given a linear objective function and a system of linear constraints; are there any known bounds on the values of (positive) integral solutions in terms of the coefficient matrix of the constraints?
...
- 111
8
votes
1
answer
236
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inferring the slope of a digitized line
Given real numbers $a$ and $b$, and an integer $n \geq 2$, let $f(n,a,b)$ be the minimum of $(nint(ja+b)-nint(ia+b)+1)/(j-i)$ (for $1 \leq i < j \leq n$) minus the maximum of $(nint(ja+b)-nint(ia+b)...
- 19.7k
4
votes
0
answers
790
views
Is it possible to use linear programming to solve this problem?
I am trying to write software to minimize pricing for cell phone subscription services, ie: choose the optimum plan for each customer in a large group.
Could someone comment on whether this is ...
- 41
3
votes
0
answers
312
views
Linear complementarity problem: principal pivoting algorithm
I'm trying to implement the "Dantzig; van de Panne and Whinston" principal pivoting algorithm for solving symmetric positive semi-definite LCPs from "The Linear Complementarity Problem" book (...
- 151
1
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0
answers
43
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Determining feasibility of specific intersection structures between closed paths in the plane
I have two arrays, each containing a different ordering of the same set of integers. Each integer is a label for a point in which two closed paths intersect in the plane. The two arrays are ...
- 11
1
vote
1
answer
272
views
Euclidean neighborhoods on Polyhedral surface
Let $(X, Vertex(X))$ be a Polyhedral surface (defined like in Polthier) , $x_0 \in X$ a vertex. Let $B_\epsilon(x_0)$ the euclidean ball centred at $x_0$ with radius $\epsilon$, $\epsilon > max ...
- 43
1
vote
1
answer
234
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Model for shipping widgets in an optimal way
I am a programmer and have the following requirement.
We are trying to figure out the optimal way to ship widgets. Below is the scenario:
We need to ship 1,000,000 widgets
We have two different size ...
- 113
2
votes
1
answer
130
views
Are there intuitive/classically algorithmic analogues to Semidefinite programs on networks?
Many network optimization algorithms, including shortest path, push-relabel, augmenting path, etc, actually have an interpretation in terms of linear programming.
A famous application of semidefinite ...
- 2,383
3
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0
answers
220
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Could SVD be used to optimize the partial inner-products?
Suppose a set $N$ of $n$ distinct points in $m-$dimensional space is given in $X\in\mathbb{R}^{n\times m}$. Also, suppose a subset $L\subset N$, $|L|=l<m<n$, with
$m-$dimensional coordinates in ...
- 131
0
votes
0
answers
104
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Big eigenvalues of a special stochastic matrix
Given a matrix $M$ of size $n\times n,$ we write its different eigenvalues by $x_1,x_2,\ldots,x_m$ with $m\leq n$ such that $|x_1|>|x_2|>|x_3|>\cdots|x_m|,$ and call $x_2\doteq |\lambda_2|(M)....
- 105
4
votes
1
answer
275
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Symmetry of the integer gap
Are there results that bound the asymmetry of the duality gap of an integer program? That is to say, if the difference between the LP solution and the IP (primal) solution is $a$, is there a function ...
- 183
1
vote
2
answers
134
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LP/QP with not-so-constant linear constaints
I have an otherwise standard LP or PSD QP problem as below:
$\min\limits_x {c}' x$ subject to $Ax\leq b$
or
$\min\limits_x \frac{1}{2}{x}' Qx + {c}' x$ subject to $Ax\leq b$
the only exception ...
- 11
1
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0
answers
126
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Matrix Minimax problem
I have the equation $\Sigma_k(M_k{p_k})V=EV$, where the $M_k$ are n*n real Hermitian matrices, $V$ is a n*n eigenvector matrix, $E$ a dim-n energy eigenvector and the $p_k$ scalar parameters. The $M_k$...
- 4,829
3
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58
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Find shift direction for min overlap area of 2 polygons
I have 2 arbitrary polygons (concave or convex) with certain overlap.
Now there is some relative shift between these 2 polygons (vector s with a constant length).
I want to find the direction of s ...
- 31
5
votes
1
answer
271
views
Feasibility of linear programs
It's known that finding the intersection of n halfplanes in 2-d takes $\Omega(n\log n)$ time. Does the lower bound apply if we change the question to deciding whether the intersection is non-empty?
- 201
0
votes
1
answer
141
views
Known graph/surface invariants that can be extracted from homology over different fields
The $Z_2$-homology of a surface viewed as a simplicial complex allows us to extract interesting invariants from the resulting homology groups. $\beta_0$ is the number of connected components, $\beta_1$...
- 4,462
2
votes
2
answers
354
views
formulate edge length problem as convex optimization problem
I want to us convex optimization to describe a problem in computational geometry.
Let $E = (E_1, E_2,\ldots , E_m) $ be a sequence of line segments in the plane, where $E_1$ and $E_m$ may be points ...
4
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0
answers
458
views
Generating random polygons from a given triangulation of points
Given a triangulation $T$ of a planar set point $S$, we would like to randomly generate a polygon (hamiltonian cycle) $P$.
However, it has been proved that Hamiltonian Circuit Problem on maximal ...
- 61
1
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0
answers
204
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Which rational subfields are corresponding to the two dimensional subspaces of holomorphic differentials
I implemented the algorithm that Felipe Voloch's suggested in his reply to the question:
Subfields of a function field
the algorithm is here:
Subfields of a function field
I considered the ...
- 601
2
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0
answers
215
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Number of breakpoints in parametric maximum flow problems
The parametric maximum flow problem can be formulated as
$$f(\lambda) = \min_{x\in\{0,1\}^n} \left( \sum_{i}(a_i + b_i\lambda)x_i + \sum_{i,j}c_{ij}x_ix_j \right),
$$
where all $c_{ij}<0$ (so that ...
- 567
1
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0
answers
58
views
Covering a set of points by bounded geometric object/objects
1) Let $S$ be a set of $n$ points in $R^d$. Now, given a bounded geometric object $G$, the problem is to check whether $S$ can be contained in $G$.
2) Also, in general setting, the problem is to ...
- 285
0
votes
1
answer
196
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Open questions in mesh generation
A mesh is a discretization of a geometric domain. An unstructured mesh is typically a triangulation. Unstructured meshes are catching up especially in the academic community.
I'm looking for open ...
5
votes
0
answers
204
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A polytope associated with the Hadamard Transform
In an investigation of whether or not a subset $V$ of "Hamming Space" $M_n = \mathbb{F}_2^n$ is a tile (i.e. whether $M_n$ can be written as a disjoint partition of translates of $V$) in http://arxiv....
- 4,636
0
votes
0
answers
103
views
Gauss-Newton for quotient functions
I'm optimizing a function of the form
$$
\sum \frac{ \|\mathbf{f_i}(x)\|^2 }{ g_i(x)^2 + h_i(x)^2 }
$$
where $x$ is a real vector, $\mathbf{f}(x)$ is a real vector, and $g(x)$ is a scalar. My first ...
- 561
2
votes
1
answer
137
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Design constraint systems over the reals
This question is inspired by the discussion at this problem.
Suppose I have a design consisting of a finite point set $U$ of size $|U|=m_{\emptyset}$ and a family of $n$ subsets (sometimes called ...
- 30.1k
2
votes
0
answers
281
views
Recovering a piecewise affine function
Lets say I have an piecewise affine convex function $f(x_1,x_2)$, on which the following operations are possible:
Computing $f(x_1,x_2)$.
Computing a subgradient to $f$ at $(x_1,x_2)$
Computing all ...
- 567
2
votes
0
answers
63
views
Put positive polynomial in finite intersection of half-spaces
This is a cross-posting of a MSE question (which did not attract any attention there so far).
Denote by $V={\mathcal P}_{n,d}$ the space of polynomials in $n$ variables with degree at most $d$, ...
- 621
0
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0
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118
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sparsest cut always has solution
Hi!
How to prove that sparsest cut always has an optimal solution which is the cut for some vertex-subset.
Looks like it's should be a kind of fundamental theorem for sparsest cut. But I didn't ...
- 1
0
votes
0
answers
79
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Computing maximum point for minimal function of a family of linear functions
Let $x \in S^n $ where $S^n = ${$ [x_1,x_2,...,x_{n+1}]\in \mathbb{R}^{n+1} \mid x \ge 0 , \sum x_i = 1 $} and let $f_i : I^n \to \mathbb{R}$ be a finite $m$-sized family of LINEAR functions such that:...
- 11
2
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0
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227
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Finding equations for projective bundles associated to vector bundles over explicitly given varieties
Suppose I have a projective variety V over a field k. It is given explicitly in terms of homogeneous equations. Moreover, say I have an explicitly given vector bundle E (in terms of a module ...
- 21
2
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0
answers
39
views
In what paper was the shrinkage parameter introduced to the nelder-mead simplex direct search algorithm?
I have read lots of papers referencing a 4th shrinkage parameter when talking about the Nelder Mead Simplex method. However, I cannot see any shrinkage parameter in the flow chart of the original ...
- 21
0
votes
0
answers
21
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Easy instance of set cover
I am trying to prove that a natural greedy algorithm solves the following instance of the set cover problem: for a set of elements $e\in U$ with a set of weights $w_e$, we define the cost of a subset ...
- 4,049