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2
votes
1answer
44 views
Explicit formula for an LMI solution
Suppose we have a linear matrix inequality (aka LMI aka spectahedron aka linear matrix pencil):
$$A_{0}+x_{1}A_{1}+x_{2}A_{2}+\ldots+x_{m}A_{m} \succeq 0.$$
(The notation $X \succeq Y$ means that ...
1
vote
0answers
15 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 ...
0
votes
0answers
31 views
Optimization with differential inequality constraint
Consider the closed set $[t_1,t_2]⊂R_{>0}$ and $V(t):[t1,t2]→R_{>0}$ being a continuous and piecewise continuously differentiable function. We want to find a continuously differentiable function ...
2
votes
0answers
74 views
existence of lattice point in polytope
This question was probably asked before but here goes. I have a convex polytope given by $Ax\leq b$ for a specific integer matrix $A$ and integer vector $b$. I need a simple method/result on how to ...
2
votes
1answer
57 views
Why does the LP Formulation of the MST Problem need Topology Constraints?
I am looking for an example that demonstrates the necessity of either subtour-elimination or of connectivity constraints in the LP formulation of the MST
In the internet I only could find the LP ...
0
votes
2answers
93 views
Rewrite optimization objective
Hi,
I wanted to ask, under which conditions can one rewrite the optimization objective
$\min_x f(x)\;\;\;s.t.\;\;\;g(x) \leq s$
as
$\min_x g(x)\;\;\;s.t.\;\;\;f(x) \leq t$
I have particular ...
1
vote
2answers
163 views
Name of operations on two vectors
Suppose we have two vectors $x\in \mathbb{R}^n$ and $y\in \mathbb{R}^m$.
I could define the mapping
$$
T: \mathbb{R}^n\times \mathbb{R}^m \rightarrow \mathbb{R}^{n\times m}
$$
as follows
$$
T(x,y) = ( ...
1
vote
0answers
38 views
LP constraint enconding
I have an objective function to be maximized
$obj(x) = \sum_i \gamma_i x_i$ with $x_i \in \mathbb{R}$
With multiple constraints of the form:
$\min_{y \in 0,1} (\sum_{i \in A} \alpha_i x_i + \sum_{i ...
0
votes
1answer
110 views
What does “Vertex Solution” mean?
Hello!
I come across the word "vertex solution" in the context
" We can also assume that x and y are vertex solutions,so that the sequence {x,y} remains in a finite set."
Could anybody know any ...
0
votes
0answers
66 views
Uniqueness result
For a standard linear programming problem, let $V$ be a real Hilbert space, $v\in V$ being fixed. $C$ a convex subset of $V$. What is the condition we have to impose on $u$ and $C$, so that the ...
2
votes
0answers
36 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 $d$, ...
1
vote
0answers
52 views
Fastest 'Oracle' Algorithm for satisfying a single linear constraint on a convex set?
In this paper by Arora, Hazan, and Kale (http://www.cs.princeton.edu/~arora/pubs/MWsurvey.pdf) a method is given for using the Multiplicative Weights Update algorithm to quickly solve Linear Programs ...
1
vote
0answers
134 views
Reference Request for Integer factorization with LP/ILP
Have there been attempts to factor integers with Linear Programming?
Searching the internet suggests that for Integer Factorization only Number Theoretic algorithms, like sieves, are taken into ...
0
votes
0answers
130 views
If-then-else on mixed linear integer programming
Hi all.
Let A,B and C be three real variables. I must write the following if-then-else condition with linear inequalities:
if A≤B then C=0 else C=B-A
Is this possible by adding a single binary ...
0
votes
2answers
162 views
Efficient algorithm finding 'a' solution of system of linear inequalities
I'm working on rational number field $\mathbb{Q}$.
Is there an efficient algorithm finding a solution of system of linear inequalities?
In many computer algebra systems like Sage or Maple,
there ...
