Publications

2018

  • Convex Hull Formulations for Mixed-Integer Multilinear Functions [arXiv]
    H. Nagarajan, K. Sundar, H. Hijazi, R. Bent
    Proceedings of the XIV International Global Optimization Workshop
    LeGO 18, Leiden, Netherlands

  • An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs [arXiv]
    H. Nagarajan, M. Lu, S. Wang, R. Bent, K. Sundar
    Journal of Global Optimization (Under review)

  • Probabilistic N-k Failure-identification for Power Systems [arXiv] [online]
    K. Sundar, C. Coffrin, H. Nagarajan, R. Bent
    Networks, Wiley online Library

  • Communication-Constrained Expansion Planning for Resilient Distribution Systems [arXiv]
    G. Byeon, P.V. Hentenryck, R. Bent, H. Nagarajan
    INFORMS Journal on Computing (Under Review)

  • Hierarchical Predictive Control Algorithms for Optimal Design and Operation of Microgrids [arXiv] [online]
    S.K.K. Hari, K. Sundar, H. Nagarajan, R. Bent, S. Backhaus
    Power Systems Computation Conference (PSCC), Dublin, Ireland

  • Tight Piecewise Convex Relaxations for Global Optimization of Optimal Power Flow [arXiv] [online]
    M. Lu, H. Nagarajan, R. Bent, S.D. Eksioglu, S.J. Mason
    Power Systems Computation Conference (PSCC), Dublin, Ireland

  • Juniper: An Open-Source Nonlinear Branch-and-Bound Solver in Julia [arXiv] [online]
    O. Kröger, C. Coffrin, H. Hijazi, H. Nagarajan
    International Conference on AI and OR Techniques in Constraint
    Programming for Combinatorial Optimization Problems (CPAIOR),
    Delft, Netherlands

  • Comparison of Various Trilinear Monomial Envelopes for Convex Relaxations of Optimal Power Flow Problems [arXiv]
    M.R. Narimani, D.K. Molzahn, H. Nagarajan, M.L. Crow
    IEEE Global Conference on Signal and Information Processing
    GlobalSIP 2018, Anaheim, CA, USA

2017

  • Optimal Transmission Line Switching under Geomagnetic Disturbances [arXiv] [online] [PPT]
    M. Lu, H. Nagarajan, E. Yamangil, R. Bent, S. Backhaus, A. Barnes
    IEEE Transactions on Power Systems

  • Resilient Off-grid Microgrids: Capacity Planning and N-1 Security [Poster] [online]
    S.C. Madathil, E. Yamangil, H. Nagarajan, A. Barnes,
    R. Bent, S. Backhaus, S.J. Mason, S. Mashayekh, M. Stadler
    IEEE Transactions on Smart Grid

  • Security-constrained Design of Isolated Multi-energy Microgrids [online]
    S. Mashayekh, M. Stadler, G. Cardoso, M. Heleno, S.C. Madathil,
    H. Nagarajan, R. Bent, M. Mueller-Stoffels, X. Lu and J. Wang
    IEEE Transactions on Power Systems

  • Ising Processing Units: Potential and Challenges for Discrete Optimization [arXiv] [PPT]
    C. Coffrin, H. Nagarajan, R. Bent
    (Under Review)

  • Adaptive Convex Relaxations for Gas Pipeline Network Optimization [online]
    F. Wu, H. Nagarajan, A. Zlotnik, R. Sioshansi, A.M. Rudkevich
    American Control Conference (ACC), Seattle, USA

  • Optimal Configurations to Minimize Disturbance Propagation in Manufacturing Networks [online]
    H. Nagarajan, P.R. Pagilla, S.Darbha, R. Bent, P.P. Khargonekar
    American Control Conference (ACC), Seattle, USA

  • Optimal Topology Design for Disturbance Minimization in Power Grids [arXiv][online]
    D. Deka, H. Nagarajan, S. Backhaus
    American Control Conference (ACC), Seattle, USA

  • Resilient Transmission Grid Design: AC Relaxation vs. DC Approximation [arXiv]
    H. Nagarajan, R. Bent, P.V. Hentenryck, S. Backhaus, E. Yamangil

2016

  • A Numerical Methodology for Enforcing Maximum Principles and the Non-Negative Constraint for Transient Diffusion Equations [arXiv] [online]
    K.B. Nakshatrala, H. Nagarajan, M. Shabouei
    Communications in Computational Physics, Cambridge University Press

  • Tightening McCormick Relaxations for Mixed-Integer Nonlinear Programs via Dynamic Multivariate Partitioning [arXiv] [online]
    H. Nagarajan, M. Lu, E. Yamangil, R. Bent
    International Conference on Principles and Practice of
    Constraint Programming, Toulouse, France

  • Optimal Resilient Transmission Grid Design [online]
    H. Nagarajan, E. Yamangil, R. Bent, S. Backhaus, P.V. Hentenryck
    Power Systems Computation Conference (PSCC), Genoa, Italy

  • Unit Commitment with N-1 Security and Wind Uncertainty [arXiv] [online]
    K. Sundar, H. Nagarajan, M. Lubin, L. Roald, S. Misra, R. Bent, D. Bienstock
    Power Systems Computation Conference (PSCC), Genoa, Italy

2015

  • Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles With Resource Constraints [online]
    H. Nagarajan, S. Rathinam, S. Darbha
    Journal of Dynamic Systems, Measurement, and Control

  • On Maximizing Algebraic Connectivity of Networks for Various Engineering Applications [online]
    H. Nagarajan, S. Rathinam, S. Darbha
    European Control Conference (ECC), Linz, Austria

2014 and earlier

  • Synthesizing Robust Networks for Engineering Applications with Resource Constraints [online]
    H. Nagarajan
    PhD Dissertation, Texas A&M University

  • Heuristics for Synthesizing Robust Networks with a Diameter Constraint [online]
    H. Nagarajan, P. Wei, S. Rathinam, D.Sun
    Mathematical Problems in Engineering, Hindawi

  • Algorithms for Finding Diameter-Constrained Graphs with Maximum Algebraic Connectivity [online]
    H. Nagarajan, S. Rathinam, S. Darbha, K.R. Rajagopal
    Dynamics of Information Systems: Mathematical Foundations

  • Algorithms for Synthesizing Mechanical Systems with Maximal Natural Frequencies [online]
    H. Nagarajan, S. Rathinam, S. Darbha, K.R. Rajagopal
    Nonlinear Analysis: Real World Applications, Elsevier

  • Enforcing the Non-negativity Constraint and Maximum Principles for Diffusion with Decay on General Computational Grids [arXiv] [online]
    H. Nagarajan, K.B. Nakshatrala
    International Journal for Numerical Methods in Fluids

  • Synthesizing Robust Communication Networks for UAVs [online]
    H. Nagarajan, S. Rathinam, S. Darbha, K.R. Rajagopal
    American Control Conference (ACC), Montréal, Canada

  • Air Transportation Network Robustness Optimization under Limited Legs Itinerary Constraint [online]
    H. Nagarajan, P. Wei, S. Rathinam, D.Sun
    International Conference on Research in Air Transportation (ICRAT),
    Berkeley, CA, USA

Collaborations

In the challenging world of Science and Engineering with increasingly complex problems, collaborative research is the key to success. I have been fortunate to have collaborated with excellent mentors and researchers over the years. Below is the list:

Name Institution Topic
Swaroop Darbha TAMU Synthesis of Robust UAV networks (thesis chair), Control Theory
Sivakumar Rathinam TAMU Synthesis of Robust UAV networks (thesis co-chair), Approximation Algorithms
K.R. Rajagopal TAMU Algebraic Connectivity in Mechanical and Biological Systems
K.B. Nakshatrala University of Houston Discrete Maximum-Minimum Principles for PDEs
Russell Bent LANL Resilient Energy Infrastructure Systems
Scott Backhaus LANL Controls and Operation of Networked Microgrids
Pascal Van Hentenryck Georgia Tech Communication-constrained Power System Resilience
Daniel Bienstock Columbia University Power Systems Operation with Wind Uncertainty
Pramod Khargonekar UC Irvine Disturbance Minimization in Linear Dynamical Systems Network
Michael Stadler LBNL, BioEnergy2020+ Design and Operation of Microgrids

Students and Postdocs

Below is the list of talented students and postdocs with whom I have really enjoyed working with:

Name Institution Duration Topic
Kaarthik Sundar LANL (Postdoc) 2015 - Present Tight Formulations for Piecewise Convex Relaxations
Mowen Lu Clemson 2016 - Present Global Optimization of Optimal Power Flow, Grid Design for Geomagnetic Disturbances (DTRA best poster award) - with Russell Bent
S.Chalil Madathil Clemson 2016 - 2018 Off-grid Microgrid Design and Operation - LANL/UNM best poster award (with Russell Bent )
Site Wang Clemson 2016 - Present POD.jl - An Open-source Solver for Global Optimization of MINLPs in Julia (with Russell Bent )
Sai Krishna TAMU 2017 - 2018 Hierarchical Model Predictive Control Algorithms for Microgrid Design and Operation (with Kaarthik Sundar )
Fei Wu Ohio State 2016 Adaptive Convex Relaxations for Gas Pipeline Network Optimization (with Anatoly Zlotnik )

Softwares

POD - An Open-source Global MINLP Solver

“POD = Piecewise convex relaxation (P) + Outer-approximation (O) + Dynamic discretization (D)” is a novel global optimization solver that uses an adaptive convexification scheme and constraint programming methods to solve Mixed-Integer Non-Linear Programs (non-convex MINLPs) efficiently. Unlike many other state-of-the-art MINLP solvers, POD is entirely built on JuMP in Julia, which provides incredible flexibility for usage and further development.

We would like to thank LANL for funding this project under the auspices of Laboratory Directed Research & Development - Exploratory Research (2017-2019).

Other useful softwares

  • MINLPLibJuMP.jl: If you are a Julia/JuMP user and looking to benchmark your algorithm on hundreds of standard MINLPs without worrying about instances being in GAMS/AMPL format, then MINLPLibJuMP.jl will be very useful.

  • Pajarito.jl: A state-of-the-art mixed-integer convex programming solver package written in Julia. And, if you are wondering what Pajarito.jl was named after, check out this link.

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