(314a) Recent Advances in the BARON Project

The BARON project for the global optimization of NLPs and MINLPs began in the early 1990s [1]. BARON has been at the forefront of the development of global optimization technology, pioneering techniques including the use of bounds tightening techniques [1, 2], polyhedral relaxations [2,3,4,5], convexity detection and use of multi-term relaxations [6,7], and multi-constraint relaxations [8,9].

In this talk, we (1) provide a brief account of key software engineering and algorithmic developments in the history of the software, (2) discuss recent advances, including the development of a systematic approach for diagnosing the cause of infeasibilities in MINLPs, acceleration via exploitation of optimality conditions, and learning approaches that result in dynamic solution strategies for solving difficult problems, and (3) present extensive computational results on a collection of benchmarks.

References cited

1. Ryoo, H. S. and N. V. Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Computers & Chemical Engineering, 19, 551-566, 1995.
2. Tawarmalani, M. and N. V. Sahinidis, Global optimization of mixed-integer nonlinear programs: A theoretical and computational study, Mathematical Programming, Ser. A, 99, 563-591, 2004.
3. M. Tawarmalani and N. V. Sahinidis, A polyhedral branch-and-cut approach to global optimization. Mathematical Programming, 103:225-249, 2005.
4. Khajavirad, A. and N. V. Sahinidis, Convex envelopes generated from finitely many compact convex sets, Mathematical Programming, 137, 371-408, 2013.
5. Khajavirad, A. and N. V. Sahinidis, Convex envelopes of products of convex and component-wise concave functions, Journal of Global Optimization, 52, 391-409, 2012.
6. Bao, X., N. V. Sahinidis, and M, Tawarmalani, Multiterm polyhedral relaxations for nonconvex, quadratically-constrained quadratic programs, Optimization Methods and Software, 24, 485-504, 2009.
7. Bao, X., A. Khajavirad, N. V. Sahinidis, and M. Tawarmalani, Global optimization of nonconvex problems with multilinear intermediates, Mathematical Programming Computation, 7, 1-37, 2015
8. Zorn, K. and N. V. Sahinidis, Computational experience with applications of bilinear cutting planes, Industrial and Engineering Chemistry Research, 52:7514-7525, 2013.
9. Zorn, K. and N. V. Sahinidis, Global optimization of general non-convex problems with intermediate bilinear substructures, Optimization Methods and Software, 29:442-462, 2014