A derivative-free trust-region algorithm with copula-based models for probability maximization problems

This work presents a derivative-free trust-region algorithm for probability maximization problems. We assume that the probability function is continuously differentiable with Lipschitz continuous gradient, but no derivatives are available. The algorithm explores the particular structure of the probability objective function through models based on copulae. Under reasonable assumptions, the global convergence of the algorithm is analyzed: we prove that all accumulation points of the sequence generated by the algorithm are stationary. The proposed approach is validated by encouraging numerical results on academic and industrial problems.