# Tagged Questions

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

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### Solving simple LP problem with Lagrange multipliers

Hi just as a test I'm trying to solve the following LP with Lagrange multipliers. $min -x_1$ $s.t$ $x_2 \leq 1 - x_1$ $x_1, x_2 \geq 0$ I add slack variables to have a equality constrained LP ...
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### Scalarization of multi-objective optimization problem (weighted sum approach)

I have an objective function where I try to minimize the quantity of bandwidth used in a network (Mbps units) - first part of the function -, minimize the CPU used in different nodes in the network (...
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### Can this optimization problem be solved?

I am working on an optimization problem but I am not sure if the problem can be formulated as an integer programming problem. Assume the cost minimization problem for a set of subscribers and ...
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### Negative bounds on variables in Linear Programming formulation

I am new to optimization theory and encountered the following problem: I am reviewing a formulation for a network problem that is fed into a mathematical solver and I noticed that on the "bounds" ...
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### Cubic Polynomial fitting with defined ranges for coefficients

Is there a way, given a set of values $(x,y)$, to find a cubic polynomial $f(x)$ that fits the values? My cubic polynomial is defined as $c_0 + c_1x +\frac {1}{2} c_2 x^2 +\frac {1}{6}c_3 x^3$ ...
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### Linear Programming: Transportation Problem with alternatives

Could someone please explain how to solve such task by linear programming: Let's say there is a starting point $A$ and two end points $B$ and $C$. $A$ is connected to $B$ and $C$ and the connections ...
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### Linear Programming: LP-Model

Let's say there are 2 types of TV shows. The first one S1 is usually watched by 2 women and 1 man. The second one S2 is watched by 1 women and 3 men. A company wants to show commercials to reach at ...
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### how to calculate slack(u,v) in the Edmond's minimum weight matching algorithm (u and v are vertices of a graph)?

I am trying to execute the Edmond's minimum weight matching algorithm. As a reference, I am using a book titled "Combinatorial Optimization Theory and Algorithms" by Bernhard Korte and Jens Vygen. The ...
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### Problem of Linear Programming, Scilab or Octave

I have to solve this with Octave or Scilab. There's an airplane company with airplanes flying to 3 different destinations (London, Paris, Rome). Schedule of flights ...
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### Polyhedron, understanding face vs facet.

I've the two following definitions, for which I was trying to understand the difference. For a given polyhedron $P$ a face $F$ is both $P$ itself or the intersection of $F$ with $P$. A facet is ...
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For $v=(v_1,...,v_n)^T \in \mathbb R^n$ we let $f(v)=|v|^2=v^Tv=v_1^2+...+v_n^2$. Show using Cauchy-Schwarz' inequality: $u^Tv \leq|u||v|$ that, $$0 \leq (1-\lambda )f(u)+\lambda f(v)-(f((1-\lambda )... 0answers 15 views ### Two phase method in linear programming suppose following tableau came after one iterations in first phase of a two phase method problem, here s_1 is a surplus variable and s_2 is a slack variable w is a artificial variable. i tried ... 5answers 101 views ### Feasible point of a system of linear inequalities Let P denote (x,y,z)\in \mathbb R^3, which satisfies the inequalities:$$-2x+y+z\leq 4x \geq 1y\geq2 z \geq 3 x-2y+z \leq 1 2x+2y-z \leq 5 How do I find an interior ...
Consider set $\mathcal{G} = \{G_1, \ldots, G_K\}$. We are given $\mathcal{A}_i \subset \mathcal{G}$, $i \in \mathcal{N}= \{1,\ldots, N\}$ and for each $\mathcal{A}_i$, there is a corresponding cost ...