This paper discusses a novel approach to nonconvex optimization which has broad-reaching applications, including those prevalent in artificial intelligence, neural networks, supervised (regression and classification) and unsupervised (clustering) machine learning, and quantum computing.
A system of methods which reaps the benefits of both grid search and random search, without their corresponding limitations, is uniquely combined with an exact method of multipliers to produce a novel approach to solving general nonconvex objective functions. At its core, independent random variables adapt themselves to produce a finer search for an extremum, according to user-defined precision specification. Because the system is gradient-free, the architecture allows for logic gates with implications for machine learning and quantum computing. Furthermore, Monte Carlo methods increase confidence in locating the global extremum facilitating verification and validation of trustable artificial intelligence.
Finally, as an example, the regression form of supervised learning (replacing neural nets with nonconvex optimization) is applied to determine the aerodynamic rolling moment coefficient based on only 20% of the data available compared with 100% of the data typically used by the method of system identification.