0
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0answers
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 ...
1
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1answer
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 ...
0
votes
1answer
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 ...
1
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1answer
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 ...
0
votes
2answers
143 views

Is an unit-cube polyhedron? What about other platonic solids?

Definitions According to my linear programming course and screenshot here (Finnish), a polyhedron is such that it can be constrained by a finite amount of inequalities such that $$P=\{\bar x\in ...
3
votes
2answers
101 views

Terminology: Linear 'programming'

What is the origin of the term 'programming' in 'linear programming'? It is not obvious to me why this should be called a type of programming.
1
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1answer
250 views

“Base is degenerate IFF its corresponding basis matrix is singular”: degenerate with solution and degenerate without solution?

Statement "Base is degenerate IFF its corresponding basis matrix is singular" is wrong according to my Linear-programming teacher Mat-2.3140 in Aalto University (translated from Finnish here/here) ...
0
votes
1answer
298 views

LP: nonbasic solution made into basic solution, help me with this terminology

Related chat here, reading the Bertsimas book now on pages 50-51. By the way, I am gathering Linear-Programming -related studying material here, welcome to read a book and have coffee :) I cannot ...
2
votes
1answer
342 views

Why we call it technological coefficients?

I'm learning linear programming's basic concepts. In following inequality: $$ \begin{align} \text{Minimize }c_1x_1 + c_2x_2 + \cdots+ c_nx_n \\ \\ \text{Subject to }a_{11}x_1 + a_{12}x_2 ...
0
votes
1answer
174 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} ...
2
votes
1answer
399 views

In linear optimization, what does “AP” stand for?

I am learning algorithms, and there is a chapter which uses linear optimization methods to solve a matching problem. This is the problem definition: I find the abbreviations AP for the constraints ...