The action of Witten's topological sigma model (defined on a worldsheet, $\Sigma$, with target space an almost complex manifold denoted $X$) takes the form $$ S=\int d^2\sigma\big(-\frac{1}{4}H^{\alpha i}H_{\alpha i}+H^{\alpha }_i\partial_{\alpha}u^i+\ldots\big), \tag{2.14} $$ as shown in equation 2.14 of his paper. The auxiliary fields $H^{\alpha i}$ also obey the "self-duality" constraint $$ H^{\alpha i}={\varepsilon^{\alpha}}_{\beta} J{^{i}}_jH^{\beta j}, \tag{2.5} $$ where $\varepsilon$ and $J$ are respectively the almost complex structures of $\Sigma$ and $X$.
Now, the Euler-Lagrange equation for $H_{\alpha}^{ i}$ is given in equation 2.15 as $$ H^i_{\alpha}=\partial_{\alpha}u^i+\varepsilon_{\alpha\beta}{J^{i}}_j\partial^{\beta}u^j. \tag{2.15} $$ How does one show this? I have tried including the "self-duality" constraint in the action via Lagrange multipliers, but I have not been able to obtain the correct Euler-Lagrange equation in this way.