The so-called regularized Biot-Savart laws (RBSLs, Titov et al. 2018) provide an efficient and flexible method for modeling pre-eruptive magnetic configurations whose characteristics are constrained by observational image and magnetic-field data. This method allows one to calculate the field of magnetic flux ropes (MFRs) with small circular cross-sections and an arbitrary axis shape. The field of the whole configuration is constructed as a superposition of (1) such a flux-rope field, (2) an ambient potential field determined, for example, by the radial field component of an observed magnetogram, and (3) a so-called compensating potential field that counteracts deviations of the radial field caused by the axial current of the MFR. The RBSL kernels are determined from the requirement that the MFR field for a straight cylinder must be exactly force-free. For a curved MFR, however, the magnetic forces are generally unbalanced over the whole path of the MFR. To reduce this imbalance, we apply a modified Gauss-Newton method to minimize the magnitude of the residual magnetic forces per unit length and the unit axial current of the MFR. This is done by iteratively adjusting the MFR axis path and axial current. We then try to relax the resulting optimized configuration in a subsequent line-tied zero-beta MHD simulation toward a force-free equilibrium. By considering several examples, we demonstrate how this approach works depending on the initial parameters of the MFR and the ambient magnetic field. Our method will be beneficial for both the modeling of particular eruptive events and theoretical studies of idealized pre-eruptive magnetic configurations. This research is supported by NSF, NASA’s HSR, SBIR, and LWS Programs, and AFOSR