Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

22,851 questions
Filter by
Sorted by
Tagged with
24 views

LP relaxation of bounded knapsack problem with constraints on the item bounds

The LP relaxation of the bounded knapsack maximization problem with weights $w_i=1$ is \begin{align} &\underset{x}{\max} \sum_i c_i x_i \\ & st \sum_i x_i \leq W \\ & \forall i, 0\leq x_i \...
104 views
+50

1k views

44 views

Minimizing average distance to closest station inside a square

I have the following problem: I have a square of area M. In the square, I can place P stations however I like. After that, I link every point in the square (and on its edge) to the closest station. My ...
1 vote
42 views

Maximizing $\sum_x p(x) (f(x) - g(x) \log p(x))$ over discrete probability distribution $p(x)$

I want to solve this maximization problem over discrete probability distributions $p(x)$, where $f(x), g(x)$ are functions of $x$ and we have $g(x) > 0$. $$\sum_x p(x) (f(x) - g(x) \log p(x))$$ I ...
599 views

35 views

Isoperimetric Property/Theorem for regular/uniform 3D shapes

What I call the "Isoperimetric Property for n-sided Polygons" is that for each $n \geq 3$, the regular $n$-gon has the minimum perimeter of all $n$-gons with a given area and the maximum ...
61k views

What is a principal minor of a matrix?

I was going through the book on operation research by Hamdy A.Taha. It referred to principal minor of a hessian matrix. Can someone explain what is meant by a principal minor? Is it different from '...
27 views

59 views

Search 2D space for optimal location to "bomb".

I am having trouble even searching for references here, do to not knowing the terminology. Well, and there are so many hits that are not this but just about overlap tests. Given a 2D (floating point) ...
42 views

116 views

Calculate the normal cone to $X=\{f: [0,1] \rightarrow [0,1]\mid f \text{ increasing}\}$

Let $X:=\{f: [0,1] \rightarrow [0,1]\mid f \text{ increasing}\}$. We endow it with $L_2$ norm, and thus $X \subset L_2([0,1])$. We can show that the set $X$ is closed and thus compact, and also ...