Multi-Variate, Multi-Term, and Multi-Constraint Relaxations for Global Optimization of Nonconvex NLPs and MINLPs with BARON

The development of the BARON algorithms and software for global optimization began nearly twenty years ago.  Initially, the software integrated factorable nonlinear relaxations within a domain-reduction-based branch-and-bound algorithm.  BARON became more widely used and recognized only after nonlinear relaxations were replaced by polyhedral ones that increased its robustness and performance.  This talk focuses on the third generation of branch-and-reduce algorithms that recently started to emerge.  Based on multi-variate, multi-term, and multi-constraint relaxation techniques, these algorithms sharpen lower bounds and enhance performance.  The talk will describe a large number of novel convex/concave envelopes for such functions, and present extensive computational results with the implementation of these envelopes in BARON.