Questions tagged [linear-algebra]
The linear-algebra tag has no usage guidance.
14
questions
3
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How to reduce an LP problem already in its standard form?
Suppose we have a feasible LP problem in its standard form. From Ax=b we can directly determine some of its variables and thus we can reduce the problem.
For example, from two constraints: x+y+z=2 and ...
- 67
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0
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explain Givens rotation chain for maintaining Cholesky factorization
I'm attempting to implement the dual face algorithm from Pan's book chapter 22 (https://link.springer.com/book/10.1007/978-981-19-0147-8).
The part in question is pasted here:
Can you please explain ...
- 892
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2
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60
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Solving regularized least squares problem using black-box computation of $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T\mathbf{x}$
Let $\mathbf{A} \in \mathbb{R}^{n \times n}$. I'm working in a problem where I have a black-box algorithmic solution to compute the products $\mathbf{A}\mathbf{x}$ and $\mathbf{A}^T \mathbf{x}$ given ...
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1
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1
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Computing simplex tableu for a given basis
I found the following problem in my book.
I know that I can compute the simplex tableau , let's call it S for a basis X_b=(x_1, x2, x_5)^T as ...
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2
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1
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Finding all left inverses of a matrix
For large rectangular matrices, is this something that is easy or possible to achieve in the programming language R? Or to get all possible equations, must one solve equations by hand? I see notes ...
4
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0
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117
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Weighted nuclear norm minimization
The problem.
Let $X,A \in\mathbb{R}^{n\times m}$ and let $W\in\mathbb{R}^{nm\times nm}$ be a positive definite matrix. I want to know if there is a closed-form solution to this problem
$$
\min_{X} \...
- 215
2
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1
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370
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Can't understand K-Truss Graph properties
Cross-posted on Mathematics SE.
Since I have to implement an algorithm in the language of linear algebra, I'm trying to understand K-Truss Graphs which are defined as such
The k-truss is a subset of ...
- 131
1
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1
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2k
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complexity order of the interior point method
I was wondering why the complexity order of the interior point method is O()^3 or O()^3.5?
Much appreciate your time and consideration.
4
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1
answer
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Algorithms for sparse linear systems
I've long wondered this, but what is the algorithm(s) implemented in modern linear equation solvers for sparse systems?
The obvious answer I can think of is Gauss-Jordan with a bunch of tricks to make ...
- 11.9k
3
votes
2
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273
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Convexity of a function
I would like to show that this function
$$2x^2 + 8y^2$$
is convex or concave by using the definition
$$f(θx+(1−θ)y) \le θf(x)+(1−θ)f(y)$$
From my understanding, using the Hessian matrix, I believe ...
- 135
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2
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Convexity of a QP
In quadratic programming (QP), you encounter an objective of the following form:
$$x^TQx + c^Tx$$
and often it's desirable to know if the QP is convex. One method to check for convexity is by ...
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19
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4
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PhD-level textbooks on linear programming
My graduate Linear Programming class uses Bertsimas & Tsitsiklis's Introduction to Linear Optimization. Are there any alternative texts that I could use to supplement this textbook (mainly the ...
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1
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IPOPT with HSL vs MUMPS
What are the advantages (if any) of using IPOPT with HSL vs MUMPS? HSL has a reputation of being faster, but does it walk the walk? In particular, does HSL scale better for large-scale problems?
We ...
- 11.9k
12
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1
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Simplest way to eliminate redundant constraints due to a new cut
I have a polyhedral set for constraining $x$:
\begin{align}
\mathcal{P} = \{x \in \mathbb{R}^n_{+} : \ Dx \leq d \}
\end{align}
where $D \in \mathbb{R}^{m \times n}, d \in \mathbb{R}^m$. I find the ...
- 3,980