An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equationJ×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representationx=x(&rgr;, &thgr;, &zgr;). Here, &thgr; are &zgr; are poloidal and toroidal flux coordinate angles, respectively, andp=p(&rgr;) labels a magnetic surface. Ordinary differential equations in &rgr; are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition ofx. A steepest‐descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive‐definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter &lgr; is introduced to ensure the rapid convergence of the Fourier series forx, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self‐consistent value for &lgr;.