# Tag Info

### In linear programming, is there a way to constrain two variables to not have opposite sign

I don't think it is possible in general. If we introduce variables $t_i$, we can write the problem as: $\max ...$ s.t. $x_i \ge t_i$ $y_i \ge 0$ $x_{min} \le t_i \le 0$ $y_it_i = 0$ (this ...
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### Solving a linear program with an active set method

Yes, it would be called the Simplex algorithm. An active set method for solving Quadratic Programming problems is often called a "Simplex algorithm" (which is as opposed to an Interior Point method).
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### Linear system with an l1-norm constraint

The set of $x$ such that $|x_{1}| \geq \sum_{i=2}^{n} | x_{i} |$ is a non-convex set, but it's relatively easy to look for solutions where $x_{1} \geq \sum_{i=2}^{n} | x_{i} |$ and then look for ...
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### Find a solution of large system of inequalities

The goal is to compute an $x\in\mathbb{R}^{n}$ to satisfy the strict inequalities $$f(z_{i})^{T}x>0\qquad\forall z_{i}\in\{1,\ldots,m\}.\tag{1}$$ If we write $\epsilon>0$ as the smallest ...
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### Getting Extremal Rays of Cone

You can use a randomized approach to solve this, as I mentioned in the comments. Ultimately, we have the equality constraint for our solution vector $\lambda$ being $A \lambda = \boldsymbol{0}$, for ...
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### Is it more efficient to capture many constraints in one constraint?

I'd recommend setting each variable to 0, rather than trying to do something clever. This is for two reasons: You might be too clever and make a mistake. For instance, setting each variable to zero ...
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### Is there a name for this integer linear optimization problem?

This is a minimum cost network flow problem. Construct the network as follows. You haven't specified the ranges for $i$ and $j$, but I'll assume that we $i=1, 2, \ldots, m$ and $j=1, 2, \ldots, n$. ...
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### Linear programming with stochasticity?

There is a huge literature on "stochastic programming", but you're probably interested in what is called "chance constrained programming", in which the constraint coefficients are random variables, ...
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### Modeling a quadratic constraint with a linear expression

Suppose $$z_{i} = x_{i} \times y_{i}$$ The constraint $$\sum_{i=1}^{n} x_{i}y_{i}\le 1$$ can be reformulated as linear constraints: 1) $$\sum_{i=1}^{n} z_{i}\le 1$$ 2) $$z_{i}\le x_{i}$$ 3) ...

### What's the fastest software(open source) to solve mixed integer programming problem

I'd recommend SCIP or HiGHS (www.highs.dev). On the industry standard benchmarks (http://plato.asu.edu/bench.html) their relative performance is similar, but on specific classes of MIPs one may be ...
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### Maximum Constraints Satisfaction of Linear Programming

For debugging purposes, it's helpful to identify small subsets of infeasible constraints in an LP formulation- an Irreducible Infeasible Subset (IIS) is a subset of the constraints that are infeasible ...
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### Python solvers for MINLP in Pyomo in Google Colab

There are so many MINLP solvers out there that this isn't really a well-defined question. Anyway, here's how you can get some: ...
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### In linear programming, is there a way to constrain two variables to not have opposite sign

When we "Plot" the region covered by a Pair of $(x,y)$ variables , we can see that it is Non-Convex , hence Linear Programming can not work out. With that Point , we have couple of ...
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### In linear programming, how can I specify a lower bound for the positive entries in the decision vector

You have a disjunctive inequality which may be expressed as $[z=0,x \leq 0] \vee [z=1,x \geq 5]$. This is non-convex, so cannot be expressed as an LP. But as you suggest, there is a way to formulate ...
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