Questions tagged [linear-algebra]

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3
votes
2answers
221 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 ...
9
votes
2answers
290 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 ...
18
votes
4answers
898 views

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 ...
17
votes
1answer
634 views

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 ...
12
votes
1answer
221 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 ...