# Questions tagged [optimization]

Questions about problems that entail selecting the best element from some set of available alternatives, and methods to solve them.

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### In s-t directed graph, how to find many small cuts?

Solving the maximum flow problem yields one qualified minimal cut. But I want several (maybe hundreds) small cuts as candidates. The cuts don't have to be minimum cuts, as long as they are small (in ...
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### BFGS vs L-BFGS — how different are they really?

I am trying to implement an optimization procedure in Python using BFGS and L-BFGS in Python, and I am getting surprisingly different results in the two cases. L-BFGS converges to the proper minimum ...
105 views

### CNF form of variable assignment problem

There are n variables $x_1$, $x_2$,..., $x_n$ and each one of them takes values from 1 to k (k>= n) and all are distinct. How can I represent this in the CNF form? (I tried the trivial way of trying ...
283 views

### Are coevolutionary “Free Lunches” really free lunches?

In their paper "Coevolutionary Free Lunches" David Wolpert and William Macready describe a set of exceptions to the No Free Lunch theorems they proved in an earlier paper. The exceptions involve two-...
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### Weighted interval scheduling with m-machines

I am looking for some advice and direction on solving the weighted interval scheduling problem with $m$-machines to plan some experimental "wet lab" procedures. The problem is very similar to the ...
168 views

### Hardness of a constrained quadratic maximization

Consider the following quadratic maximization: \begin{align} \max_{\mathbf{x} \in \mathcal{X}} &\quad\mathbf{x}^{T}\mathbf{A}\mathbf{x} \end{align} with \begin{align} \mathcal{X} = \lbrace \mathbf{...
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### Greedy strategy for computing the minimum number of rays that hit all balloons

The minimum zap problem below is Exercise 11 in Jeff Erickson's lecture on "Greedy Algorithm". The minimum zap problem can be stated more formally as follows. Given a set $C$ of $n$ circles in the ...
192 views

### Algorithms for curve construction

I am interested in algorithms that construct continuous curves between two points in such a way that minimizes an energy functional of the curve. What sort of algorithms are most used for such tasks? ...