We examine a reciprocating heat engine which necessarily operates far from equilibrium and about an unstable steady state. The piston of the engine is driven by the nonlinear coupling of the working fluid to an external light source which provides high quality heat and to the environment into which waste heat is dumped. We determine the piston trajectories that optimize two different criteria of process performance, the maximization of work output, and the minimization of entropy production. The trajectories optimizing different performance goals are qualitatively different. In engines not dominated by friction losses, the cycle optimizing work output requires that the expansion stroke begins with a slight compression and the temperature of the working fluid increases briefly.