# Questions tagged [linear-programming]

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

3,299 questions
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### stochastic optimisation of asset allocation over time

I have a problem where I'm trying to optimise the allocation of funds between a number of projects $P_1, \cdots, P_M$, each of which has an objective $O_1, \cdots, O_M$. Not only this, but I have an ...
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### Lagrange multipliers and the Simplex Algorithm

I am trying to understand the Simplex Algorithm from a gradient perspective, and I am wondering if anyone knows of a method for determining the variables that should both enter and leave the basis of ...
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### Linear programming - value of non-basic variables for the solution of a non-standard linear program

Considering this non-standard linear program: \begin{matrix} \displaystyle \min_x & c^T x \\ \textrm{s.t.} & A x & = & b \\ & x_i & \geq & 0 & & ...
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### Convex Hull of Rational Polyhedra, intersected with whole numbers

I am currently reading into polytope theory, and stumbled upon the following proposition, which I do not really understand: Let $$P = \{ x \in \mathbb{R}^{k+l} \mid Ax\leq b\}$$ be a rational ...
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### Linear programming over integers mod 2, expressing function as sum of two

Let $h=a+\ell+1$ and define $$f(a,\ell;u_2,u_1,\rho,n) = \frac{h^2}2 u_2 +h(a+\frac12)u_1+\frac{a(a+1)}2 \rho+n$$ where all the variables are integers, and such that $u_1=u_2 \pmod{2}$. Such $f$ is ...
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