## 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

**Higher-Order Newton Methods with Polynomial Work per Iteration**

A. A. Ahmadi, A. Chaudhry, J. Zhang*Submitted, 2023*

[pdf]

**Safely Learning Dynamical Systems**

A. A. Ahmadi, A. Chaudhry, V. Sindhwani, S. Tu*Submitted, 2023*

[pdf]

**A Sum of Squares Characterization of Perfect Graphs**

A. A. Ahmadi, C. Dibek*To appear in the SIAM Journal on Applied Algebra and Geometry, 2023*

[pdf]

**Learning Dynamical Systems with Side Information**

A. A. Ahmadi and B. El Khadir*SIAM Review (Research Spotlight paper), 2023**Shorter version appeared in Learning for Dynamics and Control, 2020*

[pdf]

**Sums of Separable and Quadratic Polynomials**

A. A. Ahmadi, C. Dibek, and G. Hall*Mathematics of Operations Research, 2022*

[pdf]

**Complexity Aspects of Local Minima and Related Notions**

A. A. Ahmadi and J. Zhang*Advances in Mathematics, 2022*

[pdf], slides

**On the Complexity of Finding a Local Minimizer of a Quadratic Function over a Polytope**

A. A. Ahmadi and J. Zhang*Mathematical Programming, 2022*

[pdf]

**Safely Learning Dynamical Systems from Short Trajectories**

A. A. Ahmadi, A. Chaudhry, V. Sindhwani, S. Tu*Learning for Dynamics and Control, 2021*

[pdf]

**A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics**

A. Majumdar, G. Hall, and A. A. Ahmadi*Annual Reviews in Control, Robotics, and Autonomous Systems, 2020*

[pdf]

**Time-Varying Semidefinite Programs**

A. A. Ahmadi and B. El Khadir*Mathematics of Operations Research, 2021*

[pdf]

**On the Complexity of Detecting Convexity over a Box**

A. A. Ahmadi and G. Hall*Mathematical Programming, 2019*

[pdf]

**Robust-to-Dynamics Optimization**

A. A. Ahmadi and O. Gunluk*Under review, 2022*

[pdf]

**On the Construction of Converging Hierarchies for Polynomial Optimization based on Certificates of Global Positivity**

A. A. Ahmadi and G. Hall*Mathematics of Operations Research, 2019*

[pdf]**[Young Researchers' Prize of the INFORMS Optimization Society]**

**DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization**

A. A. Ahmadi and A. Majumdar*SIAM Journal on Applied Algebraic Geometry, 2019*

[pdf]

(Related news article by Quanta Magazine)

(Related rebuttal: [pdf])

**On the Complexity of Testing Attainment of the Optimal Value in Nonlinear Optimization**

A. A. Ahmadi and J. Zhang*Mathematical Programming, 2019*

[pdf]

**A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function**

A. A. Ahmadi and B. El Khadir*Systems & Control Letters, 2018*

[pdf]

**On Algebraic Proofs of Stability for Homogeneous Vector Fields**

A. A. Ahmadi and B. El Khadir*IEEE Transactions on Automatic Control, 2019*

[pdf]

**Semidefinite Programming and Nash Equilibria in Bimatrix Games**

A. A. Ahmadi and J. Zhang*INFORMS Journal on Computing, 2019*

[pdf]

**Polynomial Norms**

A. A. Ahmadi, E. de Klerk, G. Hall*SIAM Journal on Optimization, 2019*

[pdf]

**SOS-Convex Lyapunov Functions and Stability of Difference Inclusions**

A. A. Ahmadi and R. M. Jungers*Submitted, 2018*

[pdf]

**Sum of Squares Polynomials and Geometry of 3D Environments**

A. A. Ahmadi, G. Hall, A. Makadia, and V. Sindhwani*Robotics: Science and Systems, 2017*

[pdf]

**Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems**

A. A. Ahmadi, Pablo A Parrilo*IEEE Transactions on Automatic Control, 2017*

[pdf]

**A Characterization of Lyapunov Inequalities for Stability of Switched Systems**

R. Jungers, A. A. Ahmadi, P. A. Parrilo, and M. Roozbehani*IEEE Transactions on Automatic Control, 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]

**Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations**

A. A. Ahmadi, G. Hall, A. Papachristodoulou, J. Saunderson, and Y. Zheng*In the Proceedings of the IEEE Conference on Decision and Control, 2017*

[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]

**Switched Stability of Nonlinear Systems via SOS-Convex Lyapunov Functions and Semidefinite Programming**

A. A. Ahmadi and R. Jungers*In the Proceedings of the IEEE Conference on Decision and Control, 2013*

[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

## 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]