Flight path optimization using nonlinear programming

A method, medium, and system to receive a mathematical model representation of performance characteristics for an aircraft and an engine combination; perform a projection based model order reduction on the mathematical model representation; eliminate, based on the projected model, fast dynamics components of the mathematical model representation; determine a reduced order model, as a differential algebraic equation, wherein algebraic equations replace the fast dynamics; set a flight path angle and a throttle level angle as a control to minimize fuel consumption for the modeled aircraft and engine combination; discretize equations of motion for the modeled aircraft and engine combination and formulate optimization equations as a nonlinear programming problem; and determine an optimal open loop control that minimizes fuel consumption for the modeled aircraft and engine combination to climb to a prescribed cruise altitude and airspeed.