Questions tagged [constraints]

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

533 questions
51 views

express constraint violation

A very simple question, what's the mathematical symbol (expression) that represents constraint violation. Specifically, we have a set of constraints R each of which taking three variables, two sets of ...
60 views

How can I show that these two problems have the same optimal solution?

How can I show that these two problems have the same optimal solution: $$\inf \{ x^TAx + b^Tx : 1-x^Tx \ge 0,\ x \in \mathbb R^n\}$$ $$\inf \{ x^TAx + b^Tx : 1-x^Tx = 0,\ x \in \mathbb R^n\}$$ when ...
740 views

Fit an ellipse with constraints

I'd like to fit an ellipse with the equation of $x^2 + ay^2 + bx + c =0$ This is basically the equation of an ellipse with no tilt and with its center on the horizontal axis. I have some ...
809 views

How to mathematically describe a loop over a set with two indexes.

I have a set of sets $G = \{D_{0,0}\,D_{0,1}\,D_{0,2}\,D_{1,0},...,D_{n,0}\,D_{n,m}\}$ What I know want to express is a constraint that for each set in $G$, if $x \in D_{0,0}$ then the statement ...
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How to mathematically describe the number of Element x in a set

I am trying to formulate the following. I have a Set A={x, y, z}, I also have a Set B, C and D, which all are subsets of A. It is not exactly defined which elements are in B, C and D. I only want to ...
369 views

Linear Programming Problem - Looking for an Explicit Solution

How can I solve a linear program of the form: $$\min c^Tx\\ \mathrm{s.t.}\ Ax=b\\ x\geq0\\$$ where $c$ is fixed. In the specific case I am looking at, $$x \in R^n$$ $A$ is an $m\times n$ ...
626 views