# Questions tagged [constraints]

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

532 questions
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### How to linearize the product of a non-binary discrete variable and a continuous variable?

Given a set $J$, I have the following constraint: $w_j = y_j u \quad \forall j \in J$ where $y_j \in \mathbb{N}$ and $u \in \mathbb{R}⁺_0$. I would like to make this constraint linear. Note: I am ...
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### Multiple constraints on quadratic programming? - How to solve?

Assume that you are using quadprog command in MATLAB/Octave and you want to minimize this objective function: $$\Phi_{min} = \frac{1}{2}X^TQX + c^TX$$ With ...
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### Finding a constraint on one variable of a multivariable function to constrain the entire function

I have a function. Now I want to let my variables only take values between 0, and 1. The problem is as follows. For what values of Y, is L(x,y) < 0. That is, without putting a further constraint ...
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### Can the simplex method be used for general monotonically increasing objective functions?

The simplex method relies on the fact that if you have a linear objective function and linear constraints, the optima must lie on one of the vertices of the simplex formed by the constraints. Let's ...
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### A convex objective function will be convex regardless of constraints?

Let's say I have a convex objective function. The boilerplate example is $z=x^2+y^2$. Now, I also have some constraint, $f(x,y)=0$. Is it true that the constrained optimization problem must be convex ...
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