Tagged Questions

16 views

Perturbation factor terminology

This is a question about usage of English. I have an inequality $a^\textsf{T}x \leq b$, where $a$, $b$, and $x$ are vectors in $\mathbb{R}^n$. Now, I want to perturb this inequality by a small amount ...
66 views

What does multilinear function mean?

A draft research paper claims that $Q(p)=1-p_1 p_2 p_3 p_4 - p_2 p_3 p_6 p_7-p_1p_2$ is multilinear where $p_i = \mathbb P(e_i)$ and $e_i$ is a basic event of a component to fail. I have learnt in LP ...
59 views

Optimum exists but not extreme point in Standard Form LP problem?

Standard form problem $$\min \bar c^T \bar x \text{ so that } A \bar x=\bar b, \bar x\geq \bar 0$$ I am thinking the point II (Finnish) i.e. optimum exists but it is not extreme point, why it ...
30 views

-$\infty$ cost in unconstrained LP problem?

I am trying to understand this lecture slide (Finnish) and the point in bold. It is a part of an OR condition, this is how I understand it. I cannot understand the optimal cost statement. Example ...
143 views

Positive semidefinite vector $\bar{x}$ as $\bar{x}>0 :=\bar{x} \lambda \bar{x}^{T}>0$?
$A \lambda A^{T}$ (quadratic form?) is used with matrices to check definiteness. What about with vectors? If I see conditions such as $\bar{x} > 0$, how can I know whether it means \$\bar{x}_{i} ...