Global Optimization
Global optimization provides the methodological core for solving difficult nonconvex and mixed-integer nonlinear models with rigorous bounds. This work develops adaptive partitioning, strong convex relaxations, and polyhedral and convex-hull formulations that focus computational effort where it most improves the global bound. The resulting algorithms support applications such as AC optimal power flow and transmission switching.
Selected publications
- INFORMS Journal on Computing, 2026
@article{guo2026tightening, title = {Tightening Quadratic Convex Relaxations for the Alternating Current Optimal Transmission Switching Problem}, author = {Guo, Cheng and Nagarajan, Harsha and Bodur, Merve}, journal = {INFORMS Journal on Computing}, volume = {38}, number = {3}, pages = {921--942}, year = {2026}, publisher = {INFORMS}, doi = {10.1287/ijoc.2023.0236}, } - Operations Research Letters, 2021
@article{sundar2021piecewise, title = {Piecewise Polyhedral Formulations for a Multilinear Term}, author = {Sundar, Kaarthik and Nagarajan, Harsha and Linderoth, Jeff and Wang, Site and Bent, Russell W.}, journal = {Operations Research Letters}, volume = {49}, number = {1}, pages = {144--149}, year = {2021}, publisher = {Elsevier}, month = jan, doi = {10.1016/j.orl.2020.12.002}, } - Journal of Global Optimization, 2019
@article{nagarajan2019adaptive, title = {An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs}, author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell W. and Sundar, Kaarthik}, journal = {Journal of Global Optimization}, volume = {74}, number = {4}, pages = {639--675}, year = {2019}, publisher = {Springer}, month = jan, doi = {10.1007/s10898-018-00734-1}, } - Power Systems Computation Conference (PSCC), Dublin, Ireland, 2018
@inproceedings{lu2018tight, title = {Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow}, author = {Lu, Mowen and Nagarajan, Harsha and Bent, Russell W. and Eksioglu, Sandra D. and Mason, Scott Jennings}, booktitle = {Power Systems Computation Conference (PSCC)}, location = {Dublin, Ireland}, pages = {1--7}, year = {2018}, publisher = {IEEE}, month = jun, doi = {10.23919/PSCC.2018.8442456}, } - Principles and Practice of Constraint Programming (CP), Toulouse, France, 2016
@inproceedings{nagarajan2016tightening, title = {Tightening {McCormick} Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning}, author = {Nagarajan, Harsha and Lu, Mowen and Yamangil, Emre and Bent, Russell W.}, booktitle = {Principles and Practice of Constraint Programming (CP)}, location = {Toulouse, France}, series = {Lecture Notes in Computer Science}, volume = {9892}, pages = {369--387}, year = {2016}, publisher = {Springer}, month = sep, doi = {10.1007/978-3-319-44953-1_24}, }
View all 19 publications in this track newest first
- INFORMS Journal on Computing, 2026
@article{guo2026tightening, title = {Tightening Quadratic Convex Relaxations for the Alternating Current Optimal Transmission Switching Problem}, author = {Guo, Cheng and Nagarajan, Harsha and Bodur, Merve}, journal = {INFORMS Journal on Computing}, volume = {38}, number = {3}, pages = {921--942}, year = {2026}, publisher = {INFORMS}, doi = {10.1287/ijoc.2023.0236}, } - GRIP: Reinforcement Learning-guided Iterative Partitioning for Global Optimization of QCQPsAAAI Conference on Artificial Intelligence (AAAI 2027)
@article{castellano2026grip, title = {{GRIP}: Reinforcement Learning-guided Iterative Partitioning for Global Optimization of {QCQPs}}, author = {Castellano, Agustin and Nagarajan, Harsha}, journal = {AAAI Conference on Artificial Intelligence (AAAI 2027)}, year = {2026}, } - LAP: Learning-Augmented Partitioning for Accelerating Global Optimization of Nonconvex QCQPsAAAI Conference on Artificial Intelligence (AAAI 2027)
@article{meng2026lap, title = {{LAP}: Learning-Augmented Partitioning for Accelerating Global Optimization of Nonconvex {QCQPs}}, author = {Meng, Dekang and Nagarajan, Harsha and Tanneau, Mathieu and Bent, Russell W. and Van Hentenryck, Pascal}, journal = {AAAI Conference on Artificial Intelligence (AAAI 2027)}, year = {2026}, } - Quantum
@article{nagarajan2025provably, title = {Provably Optimal Quantum Circuits with Mixed-Integer Programming}, author = {Nagarajan, Harsha and Szabo, Zsolt}, journal = {Quantum}, year = {2025}, month = oct, } - INFORMS Journal on Computing, 2025
@article{kannan2025strong, title = {Strong Partitioning and a Machine Learning Approximation for Accelerating the Global Optimization of Nonconvex {QCQPs}}, author = {Kannan, Rohit and Nagarajan, Harsha and Deka, Deepjyoti}, journal = {INFORMS Journal on Computing}, volume = {38}, number = {5}, pages = {1323--1343}, year = {2025}, publisher = {INFORMS}, month = sep, doi = {10.1287/ijoc.2023.0424}, } - Computational Optimization and Applications, 2025
@article{cengil2025tightening, title = {Learning to Accelerate Tightening of Convex Relaxations of the {AC} Optimal Power Flow Problem}, author = {Cengil, Fatih and Nagarajan, Harsha and Bent, Russell W. and Eksioglu, Sandra D. and Eksioglu, Burak}, journal = {Computational Optimization and Applications}, volume = {92}, number = {3}, pages = {761--786}, year = {2025}, publisher = {Springer}, month = aug, doi = {10.1007/s10589-025-00715-7}, } - 62nd IEEE Conference on Decision and Control (CDC), Singapore, 2023
@inproceedings{sundar2023optimization, title = {Optimization-Based Bound Tightening using a Strengthened {QC}-Relaxation of the Optimal Power Flow Problem}, author = {Sundar, Kaarthik and Nagarajan, Harsha and Misra, Sidhant and Lu, Mowen and Coffrin, Carleton and Bent, Russell W.}, booktitle = {62nd IEEE Conference on Decision and Control (CDC)}, location = {Singapore}, pages = {4598--4605}, year = {2023}, publisher = {IEEE}, doi = {10.1109/CDC49753.2023.10384116}, } - Electric Power Systems Research, 2022
@article{cengil2022learning, title = {Learning to Accelerate Globally Optimal Solutions to the {AC} Optimal Power Flow Problem}, author = {Cengil, Fatih and Nagarajan, Harsha and Bent, Russell W. and Eksioglu, Sandra D. and Eksioglu, Burak}, journal = {Electric Power Systems Research}, note = {Presented at the 2022 Power Systems Computation Conference (PSCC), Porto, Portugal}, volume = {212}, pages = {108275}, year = {2022}, publisher = {Elsevier}, month = jul, doi = {10.1016/j.epsr.2022.108275}, } - Optimization and Engineering, 2021
@article{sundar2021sequence, title = {Sequence of Polyhedral Relaxations for Univariate Functions}, author = {Sundar, Kaarthik and Sanjeevi, Sujeevraja and Nagarajan, Harsha}, journal = {Optimization and Engineering}, volume = {23}, number = {2}, pages = {877--894}, year = {2021}, publisher = {Springer}, month = feb, doi = {10.1007/s11081-021-09609-z}, } - Operations Research Letters, 2021
@article{sundar2021piecewise, title = {Piecewise Polyhedral Formulations for a Multilinear Term}, author = {Sundar, Kaarthik and Nagarajan, Harsha and Linderoth, Jeff and Wang, Site and Bent, Russell W.}, journal = {Operations Research Letters}, volume = {49}, number = {1}, pages = {144--149}, year = {2021}, publisher = {Elsevier}, month = jan, doi = {10.1016/j.orl.2020.12.002}, } - Power Systems Computation Conference (PSCC), Virtual, 2020
@inproceedings{gopinath2020proving, title = {Proving Global Optimality of {ACOPF} Solutions}, author = {Gopinath, Smitha and Hijazi, Hassan L. and Weisser, Tillmann and Nagarajan, Harsha and Yetkin, Mertcan and Sundar, Kaarthik and Bent, Russell W.}, booktitle = {Power Systems Computation Conference (PSCC)}, location = {Virtual}, volume = {189}, pages = {106688}, year = {2020}, publisher = {Elsevier}, month = jun, doi = {10.1016/j.epsr.2020.106688}, } - IEEE Transactions on Control of Network Systems, 2020
@article{garcia2020generalized, title = {Generalized Convex Hull Pricing for the {AC} Optimal Power Flow Problem}, author = {Garcia, Manuel and Nagarajan, Harsha and Baldick, Ross}, journal = {IEEE Transactions on Control of Network Systems}, volume = {7}, number = {3}, pages = {1500--1510}, year = {2020}, publisher = {IEEE}, month = mar, doi = {10.1109/TCNS.2020.2982572}, } - Journal of Global Optimization, 2019
@article{nagarajan2019adaptive, title = {An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs}, author = {Nagarajan, Harsha and Lu, Mowen and Wang, Site and Bent, Russell W. and Sundar, Kaarthik}, journal = {Journal of Global Optimization}, volume = {74}, number = {4}, pages = {639--675}, year = {2019}, publisher = {Springer}, month = jan, doi = {10.1007/s10898-018-00734-1}, } - IEEE Global Conference on Signal and Information Processing (GlobalSIP), Anaheim, CA, 2018
@inproceedings{narimani2018comparison, title = {Comparison of Various Trilinear Monomial Envelopes for Convex Relaxations of Optimal Power Flow Problems}, author = {Narimani, Mohammad Rasoul and Molzahn, Daniel K. and Nagarajan, Harsha and Crow, Mariesa L.}, booktitle = {IEEE Global Conference on Signal and Information Processing (GlobalSIP)}, location = {Anaheim, CA}, pages = {865--869}, year = {2018}, publisher = {IEEE}, month = nov, doi = {10.1109/GlobalSIP.2018.8646323}, } - XIV International Global Optimization Workshop (LeGO), Leiden, Netherlands, 2018
@inproceedings{nagarajan2018convex, title = {Convex Hull Formulations for Mixed-Integer Multilinear Functions}, author = {Nagarajan, Harsha and Sundar, Kaarthik and Hijazi, Hassan L. and Bent, Russell W.}, booktitle = {XIV International Global Optimization Workshop (LeGO)}, location = {Leiden, Netherlands}, volume = {2070}, pages = {020037}, year = {2018}, publisher = {AIP Publishing}, month = sep, doi = {10.1063/1.5090004}, } - International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR), Delft, Netherlands, 2018
@inproceedings{kroger2018juniper, title = {Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in {Julia}}, author = {Kröger, Ole and Coffrin, Carleton and Hijazi, Hassan L. and Nagarajan, Harsha}, booktitle = {International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR)}, location = {Delft, Netherlands}, series = {Lecture Notes in Computer Science}, volume = {10848}, pages = {377--386}, year = {2018}, publisher = {Springer}, month = jun, doi = {10.1007/978-3-319-93031-2_27}, } - Power Systems Computation Conference (PSCC), Dublin, Ireland, 2018
@inproceedings{lu2018tight, title = {Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow}, author = {Lu, Mowen and Nagarajan, Harsha and Bent, Russell W. and Eksioglu, Sandra D. and Mason, Scott Jennings}, booktitle = {Power Systems Computation Conference (PSCC)}, location = {Dublin, Ireland}, pages = {1--7}, year = {2018}, publisher = {IEEE}, month = jun, doi = {10.23919/PSCC.2018.8442456}, } - American Control Conference (ACC), Seattle, WA, 2017
@inproceedings{wu2017adaptive, title = {Adaptive Convex Relaxations for Gas Pipeline Network Optimization}, author = {Wu, Fei and Nagarajan, Harsha and Zlotnik, Anatoly V. and Sioshansi, Ramteen}, booktitle = {American Control Conference (ACC)}, location = {Seattle, WA}, pages = {4710--4716}, year = {2017}, publisher = {IEEE}, month = jun, doi = {10.23919/ACC.2017.7963683}, } - Principles and Practice of Constraint Programming (CP), Toulouse, France, 2016
@inproceedings{nagarajan2016tightening, title = {Tightening {McCormick} Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning}, author = {Nagarajan, Harsha and Lu, Mowen and Yamangil, Emre and Bent, Russell W.}, booktitle = {Principles and Practice of Constraint Programming (CP)}, location = {Toulouse, France}, series = {Lecture Notes in Computer Science}, volume = {9892}, pages = {369--387}, year = {2016}, publisher = {Springer}, month = sep, doi = {10.1007/978-3-319-44953-1_24}, }