# Global optimization

A plethora of problems in process synthesis, design, manufacturing, and the chemical and biological sciences require the solution of nonlinear optimization problems with multiple local solutions.

Our work in this area aims at developing an all-purpose, rigorous global optimization methodology for continuous, integer, and mixed integer nonlinear programs. Our results have included the development of: (a) a unifying framework for domain reduction which produces existing and new range-reduction techniques for integer and nonlinear programs, (b) a theory of convex extensions, which we employ to develop convex/concave envelopes of a variety of nonlinear functions, leading to the first semidefinite programming relaxation for fractional programs, (c) an entirely linear outer-approximation scheme for factorable nonlinear programs, (d) finite branching schemes for certain continuous nonconvex problem classes for which standard branch and bound approaches are merely convergent, (e) convex and concave envelopes for a variety of frequently occurring functions.

Applications of our algorithms have included molecular design, chemical process design, long range planning of chemical processes, chip layout and compaction, design of just-in-time manufacturing systems, design and analysis of metabolic and other biological systems, and control of complex chemical processes. Problems which up to recent times were thought to require advanced (such as parallel or distributed) computers for their solution, can be solved with modest hardware using our global optimization package BARON. This software has served as an enabling technology in a variety of application areas, including:

- synthesis of water networks (Ahmetovic and Grossmann, AIChE J. 57, 434-457, 2011),
- design of hybrid vehicles (Shiau and Michalek, Transactions of ASME, Journal of Mechanical Design, 133, 084502, 2011),
- modeling of microbial communities (Zomorrodi and Maranas, PLOS Computational Biology, 8, e1002363, 2012),
- portfolio selection (Cui et al., Journal of Banking & Finance, 37, 2124-2139, 2013),
- mixture design (Jonuzaj et al., AIChE J., 62, 1616-1633, 2016),
- modeling of lithium-ion batteries (Wang et al., Energy, 138, 118-132, 2017), and
- algorithm generation (Mitsos et al., Journal of Global Optimization,71, 891-9123, 2018).

Currently, our efforts center around further advancing the state of the art of global optimization algorithms and offering solutions to important applications, including supply chain operations optimization and molecular design and analysis. The ultimate goal is to provide, through BARON, a precise and valuable computational tool to engineers and scientists.

## Selected publications:

- 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. - Dorneich, M. C. and N. V. Sahinidis, Global optimization algorithms for chip layout and compaction,
__Engineering Optimization__, 25:131-154, 1995. - Gutierrez, R. A. and N. V. Sahinidis, A branch-and-bound approach for machine selection in just-in-time manufacturing systems,
__International Journal of Production Research__, 34:797-818, 1996. - Sahinidis, N. V., BARON: A general purpose global optimization software package,
__Journal of Global Optimization__, 8:201-205, 1996. - Ryoo, H. S. and N. V. Sahinidis, A branch-and-reduce approach to global optimization,
__Journal of Global Optimization__, 8:107-139, 1996. - Liu, M. L. and N. V. Sahinidis, Process planning in a fuzzy environment,
__European Journal of Operational Research__, 100:142-169, 1997. - Ghildyal, V., Design and development of a global optimization system, Master's thesis, Department of Mechanical & Industrial Engineering, University of Illinois, Urbana, IL, 1997.
- VanAntwerp, J. G., R. D. Braatz, and N. V. Sahinidis, Globally optimal robust control for systems with nonlinear time-varying perturbations,
__Computers & Chemical Engineering__, 21:S125--S130, 1997. - Shectman, J. P. and N. V. Sahinidis, A finite algorithm for global minimization of separable concave programs,
__Journal of Global Optimization__, 12:1-36, 1998. - Adhya, N., M. Tawarmalani, and N. V. Sahinidis, A Lagrangian approach to the pooling problem,
__Industrial & Engineering Chemistry Research__, 38:1956-1972, 1999. - Ryoo, H. S. and N. V. Sahinidis, Analysis of bounds for multilinear functions,
__Journal of Global Optimization__, 19:403-424, 2001. - M. Tawarmalani and N. V. Sahinidis, Semidefinite relaxations of fractional programs via novel convexification techniques,
__Journal of Global Optimization__, 20:137-158, 2001. - M. Tawarmalani and N. V. Sahinidis, Convex extensions and envelopes of lower semi-continuous functions,
__Mathematical Programming__, 93:247-263, 2002. - Tawarmalani, M. and N. V. Sahinidis, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, 504 pages, Kluwer Academic Publishers, Dordrecht, Vol. 65 in "Nonconvex Optimization And Its Applications" series, 2002. Compare prices at addall.com.
- Vaia, A. and N. V. Sahinidis, Simultaneous parameter estimation and model structure determination in FTIR spectroscopy by global MINLP optimization,
__Computers & Chemical Engineering__, 27:763-779, 2003. - Ryoo, H. S. and N. V. Sahinidis, Global optimization of multiplicative programs,
__Journal of Global Optimization__, 26:387-418, 2003. - Sahinidis, N. V., M. Tawarmalani, and M. Yu, Design of alternative refrigerants via global optimization,
__AIChE J.__, 49:1761-1775, 2003. - Tawarmalani, M. and N. V. Sahinidis, Global optimization of mixed-integer nonlinear programs: A theoretical and computational study,
__Mathematical Programming__, 99:563-591, 2004. - Ahmed, S., M. Tawarmalani, and N. V. Sahinidis, A finite branch-and-bound algorithm for two-stage stochastic integer programming,
__Mathematical Programming__, 100:355-377, 2004. - Sahinidis, N. V. and M. Tawarmalani, Accelerating branch-and-bound through a modeling language construct for relaxation-specific constraints,
__Journal of Global Optimization__, 32:259-280, 2005. - Tawarmalani, M. and N. V. Sahinidis, A polyhedral branch-and-cut approach to global optimization,
__Mathematical Programming__, 103:225-249, 2005. - Chang, Y. and N. V. Sahinidis, Global optimization in stabilizing controller design,
__Journal of Global Optimization__, 38:509-526, 2007. - 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. - Samudra, A. and N. V. Sahinidis, Design of secondary refrigerants: A combined optimization-enumeration approach, in M. M. El-Halwagi and A. A. Linninger (eds.):
__Proceedings of the 7th International Conference on the Foundations of Computer-Aided Process Design, CRC Press__, pp. 879-886, 2009. - Bao, X. and N. V. Sahinidis, Finite algorithms for global minimization of separable concave programs, in T. Coleman and P. Pardalos (eds.), Workshop on Global Optimization,
__Fields Institute Communications__, Vol. 55, American Mathematical Society, pp. 17-30, 2009. - Rios, L. M. and N. V. Sahinidis, Portfolio optimization for wealth-dependent risk preferences,
__Annals of Operations Research__, 177, 63-90, 2010. - Bao, X., N. V. Sahinidis and M. Tawarmalani, Semidefinite relaxations for quadratically constrained quadratic programming: A review and comparisons,
__Mathematical Programming__, 129:129-157, 2011. - Chang, Y. and N. V. Sahinidis, Steady-state process optimization with guaranteed robust stability under parametric uncertainty,
__AIChE Journal__, 57:3395-3407, 2011. - Khajavirad, A. and N. V. Sahinidis, Convex envelopes generated from finitely many compact convex sets,
__Mathematical Programming__, 137:371-408, 2013. - 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. - Amaran, S. and N. V. Sahinidis, Global optimization of nonlinear least-squares problems by branch-and-bound and optimality constraints,
__Top__, 20:154–172, 2012. - Samudra, A. and N. V. Sahinidis, Optimization-based framework for computer-aided molecular design,
__AIChE Journal__, 59:3686-3701, 2013. - Zorn, K. and N. V. Sahinidis, Global optimization of general nonconvex problems with intermediate bilinear substructures,
__Optimization Methods and Software__, 29:442-462, 2013. - Zorn, K. and N. V. Sahinidis, Computational experience with applications of bilinear cutting planes,
__Industrial & Engineering Chemistry Research__, 52:7514-7525, 2013. - Khajavirad, A., J. J. Michalek and N. V. Sahinidis, Relaxations of factorable functions with convex-transformable intermediates,
__Mathematical Programming__, 144:107-140, 2014. - Zorn, K. and N. V. Sahinidis, Global optimization of general nonconvex problems with intermediate polynomial substructures,
__Journal of Global Optimization__, 59:673-693, 2014. - 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. - Puranik, Y. M. Kilinc, N. V. Sahinidis, T. Li, A. Gopalakrishnan, B. Besancon, and Th. Roba, Global optimization of an industrial gas network operation,
__AIChE Journal__, 62:3215-3224, 2016. - Puranik, Y. and N. V. Sahinidis, Domain reduction techniques for global NLP and MINLP optimization,
__Constraints__, 22:338-376, 2017. - Puranik, Y. and N. V. Sahinidis, Bounds tightening based on optimality conditions for nonconvex box-constrained optimization,
__Journal of Global Optimization__, 67:59-77, 2017. - Puranik, Y. and N. V. Sahinidis, Deletion presolve for accelerating infeasibility diagnosis in optimization models,
__INFORMS Journal on Computing__, 29:754-766, 2017. - Zhou, K., M. Kılınç, X. Chen, and N. V. Sahinidis, An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver,
__Journal of Global Optimization__, 70, 497-516, 2018. - Kılınç, M. and N. V. Sahinidis, Exploiting integrality in the global optimization of mixed-integer nonlinear programming problems in BARON,
__Optimization Methods and Software__, 33, 540-562, 2018. - Nohra, C. J. and N. V. Sahinidis, Global optimization of nonconvex problems with convex-transformable intermediates,
__Journal of Global Optimization__, 72, 255-276, 2018. - Cozad, A. and N. V. Sahinidis, A global MINLP approach to symbolic regression,
__Mathematical Programming__, 170, 97-119, 2018. - Liu, J., N. Ploskas, and N. V. Sahinidis, Tuning BARON using derivative-free optimization algorithms,
__Journal of Global Optimization__, 74, 611-637, 2019. - Furini, F., E. Traversi, P. Belotti, A. Frangioni, A. Gleixner, N. Gould, L. Liberti, A. Lodi, R. Misener, H. Mittelmann, N. V. Sahinidis, S. Vigerske, A. Wiegele, QPLIB: A library of quadratic programming instances,
__Mathematical Programming Computation__, 11, 237-265, 2019. - Del Pia, A., A. Khajavirad, and N. V. Sahinidis, On the impact of running intersection inequalities for globally solving polynomial optimization problems,
__Mathematical Programming Computation__, accepted, 2019.