# Tagged Questions

Questions on optimization constrained to integer variables.

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### Reference Request For Hermite normal form of non full row rank matrix

Could someone recommend me some references which discuss the problem of the reduction of a matrix which is not full row rank into its Hermite normal form?
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### Conditions for a totally unimodular coefficient matrix of a Multi-Commodity-Minimum-Cost-Flow-Problem

I'm considering the following Multi-Commodity-minimum-Cost-Flow-Problem: This leads us to a coefficient matrix $A$ with $N$ donates the incidence matrix of a directed graph and $I$ is the ...
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### What are common Mathematical Programming Languages out there?

I've seen the term used Mathematical Programming to describe a superset of: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer nonlinear ...
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### MILP optimization constraint formulation

I'm trying to find a sensible way to add constraint for my optimization problem. Lets assume we have binary decision variables $x_i\in\{0,1\}$ and two constraints \begin{align*} \sum\limits_{i=1}^n ...
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### Lenstra's integer programming algorithm: Finding a lattice point “near the center”

Preliminaries: As part of Lenstra's algorithm for integer programming (see here, page 4) we compute a linear transformation $\tau$ and a point $z \in \mathbb{R}^n$ which meet certain conditions (step ...
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### Can the “goat cabbage wolf” problem be solved using integer programming?

Question: Can you solve the "goat cabbage wolf" problem using integer programming. If so could I get an outline of the solution or a reference to one?
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### What method will work for this linear programming problem?

I just started studying linear programming and I have limited resources with which to work. I have to work on a number of exercises but the notes I have do not help much so I have to look online for ...
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### Network flow as a linear/integer programming problem with special conditional constraints

Consider the classic network flow problem where the constraint is that the inflow to a vertex is equal to the sum of its outflows. Consider having a more specific constraint where the flow cannot be ...
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### Find the global/local minima of a quadratic function over the set of integer?

Sorry for my poor English, I'm trying to find the global and local minima of a quadratic function: $x^2 - 3x$, with $x \in Z$. Here is my solution: It is straightforward to find the global minima ...
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### Multiple Choice Integer Program Special Ordered Set Naming

I have been given a problem, for which I have a hard time to find literature, since I'm unsure about the right name of the problem. The problem is defined as: We have given $k$ sets and we need to ...
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### Shadow prices in assignment problems (and their relationship to Lagrange multipliers of LP-relaxation)

Lagrange multipliers for linear programs can be interpreted as shadow prices. Shadow prices typically represent marginal/differential changes in the objective from a marginal loosening of a given ...
I have the following optimization problem: Model I: $$f(x,y) \\ s.t., \\ y\leq x+M(1-V)\\ y \leq MV \\ x \geq 0, y \geq 0$$ where x and y are continuous variables whereas V is a binary variable. M ...