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A bit late but it might help other people looking for the same answer. The package optidef ( https://www.ctan.org/pkg/optidef ) was intended as the easy way to define optimization problems.

\usepackage{optidef}
\begin{mini}|l|
{w,u}{f(w)+ R(w+6x)}{}{}
\addConstraint{g(w_k)+h(w_k)}{=0,}{k=0 ...