Optimization of process variables is an important, yet difficult, task for systems-level analysis and design of complex stochastic systems. Here, we introduce the Simplex-Triangulation Optimization (STO) algorithm to optimize stochastic black-box systems efficiently in fewer iterations than other comparable algorithms without requiring gradient information or detailed initial guesses. The STO algorithm is shown to converge linearly. Several test functions are utilized to compare the STO algorithm to the Particle Swarm Optimization (PSO) and Finite Difference Stochastic Approximation (FDSA) algorithms, which are often used for parameter optimization in stochastic systems.