Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO.

•We review the recent advances in global optimization for Mixed Integer Nonlinear Programming, MINLP.•We review the recent advances in global optimization for Constrained Derivative-Free optimization, CDFO.•We present theoretical contributions, software implementations and applications for both MINLP and CDFO.•We discuss possible interactions between the two areas of MINLP and CDFO.•We present a complete test suite for MINLP and CDFO algorithms.