Optimization problems from the industry often do not possess the necessary structure to be solved by traditional optimization methods. Indeed, the objective function and constraints defining the problem are typically provided as black boxes (i.e., a computer code that reads some variables and computes some function values). These black boxes may be costly, imprecise and may fail for some internal reasons, and computation of derivatives may be problematic. These problems are frequent in engineering and in the industry.
We will present some algorithms as well as a convergence analysis based on the Clarke generalized derivatives necessary optimality conditions.