Questions tagged [linear-algebra]

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4 votes
0 answers
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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} \...
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2 votes
1 answer
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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 ...
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1 vote
1 answer
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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.
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4 votes
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 ...
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3 votes
2 answers
258 views

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 ...
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  • 135
9 votes
2 answers
376 views

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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18 votes
4 answers
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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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16 votes
1 answer
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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 ...
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12 votes
1 answer
392 views

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 ...
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