Particle Swarm Optimization Algorithm I am studying about Particle Swarm Optimization (PSO) and I was wondering what the user-defined constants in the update equations are for. 

First update equations: 
$v(t) = w*v(t) + c_1*rand*(x_{best} - x) + c_2*rand*(g_{best} - x)$

$w$ is known as the weight/inertial constant. Usually values here are in the interval $(0,1)$. 
What are $c_1$ and $c_2$ for?

Thanks
they are known as the Learning factors: c1 and c2 usually equal to 2. However, other settings were also used in different papers. But usually c1 equals to c2 and ranges from [0, 4]

if you need more information about PSO i'd have a quick read of the tutorials at http://www.swarmintelligence.org/tutorials.php