Publications

Ph.D. Thesis
  • Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis
    A. A. Ahmadi
    PhD Thesis, Massachusetts Institute of Technology, 2011
    [pdf], [abstract]
Papers
  • On the Construction of Converging Hierarchies for Polynomial Optimization based on Certificates of Global Positivity
    A. A. Ahmadi and G. Hall

    Submitted, 2017
    [pdf]


  • Semidefinite Programming and Nash Equilibria in Bimatrix Games
    A. A. Ahmadi and J. Zhang

    Submitted, 2017
    [pdf]


  • DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
    A. A. Ahmadi and A. Majumdar
    Submitted, 2017
    [pdf]
  • Polynomial Norms
    A. A. Ahmadi, E. de Klerk, G. Hall
    Submitted, 2017
    [pdf]

  • Sum of Squares Polynomials and Geometry of 3D Environments
    A. A. Ahmadi, G. Hall, A. Makadia, and V. Sindhwani
    Accepted to RSS, 2017
    [pdf]

  • DC Decomposition of Nonconvex Polynomials with Algebraic Techniques
    A. A. Ahmadi and G. Hall
    To appear in Math Programming, 2016
    [pdf]

  • Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming
    A. A. Ahmadi and G. Hall
    Contemporary Mathematics, to appear, 2016
    [pdf]

  • Optimization over Structured Subsets of Positive Semidefinite Matrices via Column Generation
    A. A. Ahmadi, S. Dash, and G. Hall
    Discrete Optimization, to appear, 2016
    [pdf]


  • Robust-to-dynamics Optimization
    A. A. Ahmadi and O. Gunluk
    In preparation, 2017 - conference version appeared in the Proceedings of the 2015 IEEE Conference on Decision and Control.
    [slides]


  • Lower Bounds on Complexity of Lyapunov Functions for Switched Linear Systems
    A. A. Ahmadi and R. Jungers

    Nonlinear Analysis: Hybrid Systems, 2016
    [pdf]


  • Towards Scalable Algorithms with Formal Guarantees for Lyapunov Analysis of Control Systems via Algebraic Optimization
    A. A. Ahmadi and P. A. Parrilo

    Tutorial paper - to appear in the Proceedings of the 53rd
     the IEEE Conference on Decision and Control, 2014
    [pdf]


  • Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
    A. A. Ahmadi and A. Majumdar

    To appear in Optimization Letters, 2015.
    [pdf]


  • Control and Verification of High-Dimensional Systems via DSOS and SDSOS Optimization
    A. Majumdar, A. A. Ahmadi, and R. Tedrake

    To appear in the Proceedings of the 53rd
     the IEEE Conference on Decision and Control, 2014
    [pdf]


  • DSOS and SDSOS Optimization: LP and SOCP-Based Alternatives to SOS Optimization
    A. A. Ahmadi and A. Majumdar

    In the Proceedings of the 2014 Conference on Information Sciences and Systems

  • On Complexity of Lyapunov Functions for Switched Linear Systems
    A. A. Ahmadi and R. Jungers
    To appear in the Proceedings of the World Congress of the International Federation of Automatic Control, 2014 
    [pdf]


  • SOS-Convex Lyapunov Functions with Applications to Nonlinear Switched Systems
    A. A. Ahmadi and R. Jungers
    In the Proceedings of the IEEE Conference on Decision and Control, 2013 (journal version in preparation)
    [pdf]


  • Computational and Algebraic Aspects of Convexity
    Fall 2013 Newsletter of the INFORMS Computing Society
    [link to pdf]

  • Modern Optimization Tools for Complex Business and Economic Dynamics
    A. A. Ahmadi 
    In preparation, 2013    

  • Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions
    A. A. Ahmadi and P. A. Parrilo
    IEEE Transactions on Automatic Control, Submitted, 2013    
    [pdf]

  • A Complete Characterization of the Gap between Convexity and SOS-Convexity
    A. A. Ahmadi and P. A. Parrilo
    SIAM Journal on Optimization,  2013      [INFORMS Computing Society Prize 1/3 ---]
    [pdf][arXiv]


  • NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems
    A. A. Ahmadi, A. Olshevsky, P. A. Parrilo, J. N. Tsitsiklis
    Mathematical Programming ,  2013        [INFORMS Computing Society Prize 2/3 ---], [MIT News]

    [pdf], [arXiv]

  • A Convex Polynomial that Is Not SOS-Convex
    A. A. Ahmadi, P. A. Parrilo 
    Mathematical Programming , 2011      
    [INFORMS Computing Society Prize 3/3 ---]
    [pdf][arXiv]

  • Joint Spectral Radius and Path-Complete Graph Lyapunov Functions
    A. A. Ahmadi, R. Jungers, P. A. Parrilo, and M. Roozbehani
    SIAM Journal on Optimization and Control, to appear, 2014  [Best SICON Paper Prize, 2013-2015]

    [pdf][arXiv]

  • Complexity of Ten Decision Problems in Continuous Time Dynamical Systems
    A. A. Ahmadi, A. Majumdar, and R. Tedrake
    In Proceedings of the 2013 American Control Conference, 2012

    [pdf]

  • Control Design Along Trajectories via Sum of Squares Optimization
    A. Majumdar, A. A. Ahmadi, and R. Tedrake
    In Proceedings of the 2013 International Conference on Robotics and Automation, 2012

    [pdf]

  • Joint Spectral Radius of Rank One Matrices and the Maximum Cycle Mean Problem
    A. A. Ahmadi and P. A. Parrilo
    In Proceedings of the 51st IEEE Conference on Decision and Control, 2012 
    [pdf]
  • On the Difficulty of Deciding Asymptotic Stability of Cubic Homogeneous Vector fields
    A. A. Ahmadi
    In Proceedings of the American Control Conference, 2012   

    [pdf][arXiv]    [Best presentation in session on Stability of Nonlinear Systems]

  • Feasibility Checks and Control Laws for Reconfigurations of Spacecraft Clusters
    N. Moshtagh, A. A. Ahmadi, and M. Mesbahi
    In Proceedings of the American Control Conference, 2012   

    [pdf]

  • A Globally Asymptotically Stable Polynomial Vector Field with no Polynomial Lyapunov Function
    A. A. Ahmadi, M. Krstic, P. A. Parrilo
    In Proceedings of  the 50th IEEE Conference on Decision and Control, 2011
    [pdf]

  • Converse Results on Existence of Sum of Squares Lyapunov Functions
    A. A. Ahmadi, P. A. Parrilo
    In Proceedings of  the 50th IEEE Conference on Decision and Control, 2011
    [pdf] 
  • Analysis of the Joint Spectral Radius via Lyapunov Functions on Path-Complete Graphs
    A. A. Ahmadi, R. Jungers, P. A. Parrilo, M. Roozbehani
    Hybrid Systems: Computation and Control, 2011  (Book Chapter)
    [pdf]
       
  • On the Equivalence of Algebraic Conditions for Convexity and Quasiconvexity of Polynomials
    A. A. Ahmadi, P. A. Parrilo
    In Proceedings of 49th IEEE Conference on Decision and Control, 2010
    [pdf]
       
  • On Higher Order Derivatives of Lyapunov Functions
    A. A. Ahmadi, P. A. Parrilo
    In Proceedings of  the 2011 American Control Conference, Submitted in 2010
    [pdf]
       
  •  A Positive Definite Polynomial Hessian that Does not Factor
    A. A. Ahmadi, P. A. Parrilo
    In Proceedings of 48th IEEE Conference on Decision and Control, 2009
    [pdf]    
  • Non-monotonic Lyapunov Functions for Stability of Discrete Time Nonlinear and Switched Systems
    A. A. Ahmadi, P. A. Parrilo
    In Proceedings of 47th IEEE Conference on Decision and Control, 2008
    [pdf]  
        [Best Student Paper Award Finalist]

  • High-Speed Broadband Polarization-Independent Optical Clock Recovery in a Silicon Detector
    A. A. Ahmadi, R. Salem, T. E. Murphy
    The Optical Fiber Communication Conference, 2006
    [pdf]     
    [Washington Society of Engineers' Young Engineer Prize]

  • Two-Photon Absorption for Optical Clock Recovery in OTDM Networks
    R.Salem, A. A. Ahmadi, G. E. Tudury, G. M. Carter, T. E. Murphy
    IEEE Journal of Lightwave Technology, 2007
    [pdf] 

Working Papers

  • Convex Ternary Quartics are SOS-Convex
    A. A. Ahmadi, G. Blekherman, P. A. Parrilo   
  • Hardness Results and Semidefinite Relaxations for Control of Underactuated Robots
    A. Majumdar, A. A. Ahmadi, R. Tedrake
  • Non-monotonic Lyapunov Functions
    A. A. Ahmadi, P. A. Parrilo 
S.M. Thesis
  • Non-monotonic Lyapunov Functions for Stability of Nonlinear and Switched Systems: Theory and Computation
    A. A. Ahmadi
    Master's Thesis, Massachusetts Institute of Technology, 2008 
    [pdf], [official]