Questions tagged [linear-programming]

Questions on linear programming, the optimization of a linear function subject to linear constraints.

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An LP problem from David G. Luenberger's Linear and Nonlinear Programming book

Could someone help me to solve the following problem? A class of piecewise linear functions can be represented as $f(x) = Maximum (c_{1}^Tx+ d_{1}, c_{2}^Tx, \cdots, c_{p}^Tx + d_{p})$. For such a ...
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Let $V = \{v_1,v_2,..,v_n\}$ be a set of vectors in $\mathbb{R}^n$, $t$ be the target vector in $\mathbb{R}^n$ and a natural number $m > 1$. Properties about $V$ and $t$: $cos\phi(t,v_i) \geq \... 1answer 1k views How to convert linear program into standard form? Suppose I wish to solve the linear program $$\begin{array}{ll} \text{maximize} & c^T x\\ \text{subject to} & Ax \leq b\\ & x > 2016\end{array}$$ where$x>2016$means that all ... 2answers 1k views How get the extreme directions of an unbounded feasible region The following constraints form a feasible region.$-x_1+x_2 \le 2-x_1+2x_2 \le 6x_1,x_2 \ge 0$The feasible region have three extreme points:$e_1=\left[\begin{array}{cc} 0\\ 0 \end{...
I have a linear system of equations $$A(\xi)x(\xi)=b(\xi),$$ where $\xi \in \mathbb{R}_+^1$ is a parameter, $A\in\mathbb{R}^{N\times N}$ and is non-singular, and $x,b \in \mathbb{R}^N$. I would like ...