Modern structural analysis necessitates numerical formulations with advanced nonlinear attributes. To that end, numerous finite elements have been proposed, spanning from classical to hybrid standpoints. In addition to their individual features, all formulations originally stem from an underlying variational principle, which can be deemed as a unified energy metric of the system. The corresponding equations of structural equilibrium define a stationary point of the assumed principle. Following this logic in this work, the total potential energy is directly treated as an objective function, subject to some kinematic compatibility constraints, within the conceptions of nonlinear programming. The only approximated internal field is curvature, whereas displacements occur solely as nodal entities and Lagrange multipliers serve compatibility. Thereby, a new nonlinear programming hybrid element formulation is derived, which uses exact kinematic fields, can incorporate nonlinear assumptions of any extent, and is amenable to various applicable nonlinear programming algorithms. The suggested nonlinear program is presented in detail herein, together with its consistent second-order iterative solution procedure. The results obtained in benchmark nonlinear structural problems are validated and compared with OpenSees flexibility-based elements, showcasing notable performance in terms of accuracy, mesh density discretization, computational speed, and robustness.