# Questions tagged [linear-programming]

Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.

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### Linear programming question, [closed]

enter image description here A farmer has several hectares of land on which, corn, tomatoes, or peas can be grown. The gross income resulting from planting 1 hectare of each crop is shown below, ...
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### What is the effect of adding uniqueness constraints to linear programs

Question: If it is known that the optimal solution to a linear program isn't unique and it is possible to enforce uniqueness by means of additional constraints, what is the impact of adding those ...
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### How do I solve this integer programming problem with non convex constraints?

I am not sure if this is the right place to post this question, please point me to the correct forum if I posted in a wrong place. I have an optimization problem like this ...
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### Generalization of Farkas' Lemma to Hermitian Matrices

I recently stumbled upon a well-known version of Farkas' Lemma which, roughly speaking, I would like to generalize from real vectors to hermitian matrices, as it seems promising for something else I ...
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### Converting a vector in a cone statement to inequality constraints

I would like to convert the following condition for $x$ \begin{align} x = N \lambda, \lambda \geq 0 \end{align} to a pure linear inequality form, i.e. find an $L$ and eliminate $\lambda$ \begin{...
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Let $A \in \mathbb{R}^{m \times n}$. Is it true that $$\min \limits_{Q \in \mathbb{R}^{n \times m}}|I - QA|_{\infty} < \frac{1}{2}$$ is criteria for the uniqueness of the 1-sparse solution to $\... 0answers 103 views ### Prove that these linear programming problems are bounded by$O(k^{1/2})$[closed] The expanded partial sums of the Möbius inverse of the Harmonic numbers have two out of three properties in common with this set of linear programming problems: $$\begin{array}{ll} \text{minimize} &... 0answers 125 views ### What do square roots as minimums have to do with Harmonic numbers? In an earlier question where I conjectured (and GH from MO confirmed) that the von Mangoldt function is the limit at s=1 of a certain Dirichlet series:$$\Lambda(m)=\lim_{s\to 1+}\zeta(s)\sum_{d\mid ... 0answers 73 views ### Uniqueness of projection under spectral norm I am considering $$\min_{M\in \mathcal{M}} \|X - M\|:=x \neq 0,$$ where$X$,$M$are$m\times n$matrices,$\|\cdot\|$is spectral norm and$\mathcal{M}$is a matrix subspace. I wonder to what ... 1answer 174 views ### On optimal dual solutions for the minimum weight perfect matching problems in the case of metric weights Following Lovasz-Plummer (Matching theory, North-Holland 1986, Theorem 9.2.1), the minimum weight perfect matching problem on a complete graph$G$with even number of vertices and weight$w:E(G)\to \...
The Hirsch conjecture asserts that the graph (i.e. $1$-skeleton) of a $d$-dimensional convex polytope with $n$ facets has diameter at most $n - d$. After being open for decades, Francisco Santos has ...
The following linear programming problem $x_n = \arg\min c_n'x \mbox{ subject to } Ax<b$ has a changing coefficient $c_n$. We have that $c_n\rightarrow c_*$. What happens to the solution $x_n$? ...