begin{equation}
  begin{aligned}
    min_{vec{y}, vec{v}} & f(vec{y}) + g(vec{v})  \
    textrm{s.t. } &
    begin{aligned}
      dot{vec{y}} & = f(vec{y}, vec{v}) \
      vec{y}(0) & = vec{y}_0 \
    end{aligned}
  end{aligned}
end{equation}