Simple constraint

If $x_{1}$ follows $x_{0}$, then $x_{1}$ gets its coordinates from the following set of equations:

Calculate the difference in $x$ and $y$

Failed to parse (unknown function "\d"): {\displaystyle \d_p = p_0 - p_1 }

$\min f({\mathbf {x}})=x_{1}^{2}+x_{2}^{4}$

, the length of the hypothenuse

$l_{1}=d_{x}^{2}+d_{y}^{2}$

, difference with given radius, $r$

$p_{d}=d_{x}/l_{1}*r-d_{x}$

, and finally add the difference

$p_{1}+=p_{d}$