Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC, 2008)

A positive definite polynomial Hessian that does not factor. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC, 2009)

On the equivalence of algebraic conditions for convexity and quasiconvexity of polynomials. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC, 2010)

On higher order derivatives of Lyapunov functions. - Amir Ali Ahmadi; Pablo A. Parrilo (ACC, 2011)

A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function. - Amir Ali Ahmadi; Miroslav Krstic; Pablo A. Parrilo (CDC/ECC, 2011)

Converse results on existence of sum of squares Lyapunov functions. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC/ECC, 2011)

Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs. - Amir Ali Ahmadi; Raphaël M. Jungers; Pablo A. Parrilo; Mardavij Roozbehani (HSCC, 2011)

Algebraic relaxations and hardness results in polynomial optimization and Lyapunov analysis. - Amir Ali Ahmadi (2011)

On the difficulty of deciding asymptotic stability of cubic homogeneous vector fields. - Amir Ali Ahmadi (ACC, 2012)

Feasibility checks and control laws for reconfigurations of spacecraft clusters. - Nima Moshtagh; Amir Ali Ahmadi; Mehran Mesbahi (ACC, 2012)

Joint spectral radius of rank one matrices and the maximum cycle mean problem. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC, 2012)

When Is a Set of LMIs a Sufficient Condition for Stability? - Amir Ali Ahmadi; Raphaël M. Jungers; Pablo A. Parrilo; Mardavij Roozbehani (ROCOND, 2012)

Algebraic Relaxations and Hardness Results in Polynomial Optimization and Lyapunov Analysis - Amir Ali Ahmadi (CoRR, 2012)

A convex polynomial that is not sos-convex. - Amir Ali Ahmadi; Pablo A. Parrilo (Math. Program., 2012)

Complexity of ten decision problems in continuous time dynamical systems. - Amir Ali Ahmadi; Anirudha Majumdar; Russ Tedrake (ACC, 2013)

Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming. - Amir Ali Ahmadi; Raphaël M. Jungers (CDC, 2013)

Control design along trajectories with sums of squares programming. - Anirudha Majumdar; Amir Ali Ahmadi; Russ Tedrake (ICRA, 2013)

Stability of Polynomial Differential Equations: Complexity and Converse Lyapunov Questions. - Amir Ali Ahmadi; Pablo A. Parrilo (CoRR, 2013)

NP-hardness of deciding convexity of quartic polynomials and related problems. - Amir Ali Ahmadi; Alexander Olshevsky; Pablo A. Parrilo; John N. Tsitsiklis (Math. Program., 2013)

A Complete Characterization of the Gap between Convexity and SOS-Convexity. - Amir Ali Ahmadi; Pablo A. Parrilo (SIAM J. Optim., 2013)

Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization. - Amir Ali Ahmadi; Pablo A. Parrilo (CDC, 2014)

Control and verification of high-dimensional systems with DSOS and SDSOS programming. - Anirudha Majumdar; Amir Ali Ahmadi; Russ Tedrake (CDC, 2014)

DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization. - Amir Ali Ahmadi; Anirudha Majumdar (CISS, 2014)

Joint Spectral Radius and Path-Complete Graph Lyapunov Functions. - Amir Ali Ahmadi; Raphaël M. Jungers; Pablo A. Parrilo; Mardavij Roozbehani (SIAM J. Control. Optim., 2014)

Robust-to-dynamics linear programming. - Amir Ali Ahmadi; Oktay Günlük (CDC, 2015)

Sum of Squares Basis Pursuit with Linear and Second Order Cone Programming. - Amir Ali Ahmadi; Georgina Hall (CoRR, 2015)

Lower Bounds on Complexity of Lyapunov Functions for Switched Linear Systems. - Amir Ali Ahmadi; Raphaël M. Jungers (CoRR, 2015)

Some applications of polynomial optimization in operations research and real-time decision making. - Amir Ali Ahmadi; Anirudha Majumdar (Optim. Lett., 2016)

Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations. - Amir Ali Ahmadi; Georgina Hall; Antonis Papachristodoulou; James Saunderson; Yang Zheng 001 (CDC, 2017)

Geometry of 3D Environments and Sum of Squares Polynomials. - Amir Ali Ahmadi; Georgina Hall; Ameesh Makadia; Vikas Sindhwani (Robotics: Science and Systems, 2017)

Response to "Counterexample to global convergence of DSOS and SDSOS hierarchies". - Amir Ali Ahmadi; Anirudha Majumdar (CoRR, 2017)

Optimization over structured subsets of positive semidefinite matrices via column generation. - Amir Ali Ahmadi; Sanjeeb Dash; Georgina Hall (Discret. Optim., 2017)

Sum of Squares Certificates for Stability of Planar, Homogeneous, and Switched Systems. - Amir Ali Ahmadi; Pablo A. Parrilo (IEEE Trans. Autom. Control., 2017)

A Characterization of Lyapunov Inequalities for Stability of Switched Systems. - Raphaël M. Jungers; Amir Ali Ahmadi; Pablo A. Parrilo; Mardavij Roozbehani (IEEE Trans. Autom. Control., 2017)

Some Recent Directions in Algebraic Methods for Optimization and Lyapunov Analysis. - Amir Ali Ahmadi; Pablo A. Parrilo (Geometric and Numerical Foundations of Movements, 2017)

SOS-Convex Lyapunov Functions and Stability of Difference Inclusions. - Amir Ali Ahmadi; Raphaël M. Jungers (CoRR, 2018)

DC decomposition of nonconvex polynomials with algebraic techniques. - Amir Ali Ahmadi; Georgina Hall (Math. Program., 2018)

A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function. - Amir Ali Ahmadi; Bachir El Khadir (Syst. Control. Lett., 2018)

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics. - Anirudha Majumdar; Georgina Hall; Amir Ali Ahmadi (CoRR, 2019)

On the Construction of Converging Hierarchies for Polynomial Optimization Based on Certificates of Global Positivity. - Amir Ali Ahmadi; Georgina Hall (Math. Oper. Res., 2019)

DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization. - Amir Ali Ahmadi; Anirudha Majumdar (SIAM J. Appl. Algebra Geom., 2019)

Polynomial Norms. - Amir Ali Ahmadi; Etienne de Klerk; Georgina Hall (SIAM J. Optim., 2019)

Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics. - Anirudha Majumdar; Georgina Hall; Amir Ali Ahmadi (Annu. Rev. Control. Robotics Auton. Syst., 2020)

Complexity aspects of local minima and related notions. - Amir Ali Ahmadi; Jeffrey Zhang 002 (CoRR, 2020)

On the complexity of detecting convexity over a box. - Amir Ali Ahmadi; Georgina Hall (Math. Program., 2020)

On the complexity of testing attainment of the optimal value in nonlinear optimization. - Amir Ali Ahmadi; Jeffrey Zhang 002 (Math. Program., 2020)

On Algebraic Proofs of Stability for Homogeneous Vector Fields. - Amir Ali Ahmadi; Bachir El Khadir (IEEE Trans. Autom. Control., 2020)

Safely Learning Dynamical Systems from Short Trajectories. - Amir Ali Ahmadi; Abraar Chaudhry; Vikas Sindhwani; Stephen Tu (L4DC, 2021)

Semidefinite Programming and Nash Equilibria in Bimatrix Games. - Amir Ali Ahmadi; Jeffrey Zhang 002 (INFORMS J. Comput., 2021)

Time-Varying Semidefinite Programs. - Amir Ali Ahmadi; Bachir El Khadir (Math. Oper. Res., 2021)

On the complexity of finding a local minimizer of a quadratic function over a polytope. - Amir Ali Ahmadi; Jeffrey Zhang 002 (Math. Program., 2022)

Safely Learning Dynamical Systems. - Amir Ali Ahmadi; Abraar Chaudhry; Vikas Sindhwani; Stephen Tu (CoRR, 2023)

Higher-Order Newton Methods with Polynomial Work per Iteration. - Amir Ali Ahmadi; Abraar Chaudhry; Jeffrey Zhang 002 (CoRR, 2023)

Learning Dynamical Systems with Side Information. - Amir Ali Ahmadi; Bachir El Khadir (SIAM Rev., 2023)

Sums of Separable and Quadratic Polynomials. - Amir Ali Ahmadi; Cemil Dibek; Georgina Hall (Math. Oper. Res., 2023)

A Sum of Squares Characterization of Perfect Graphs. - Amir Ali Ahmadi; Cemil Dibek (SIAM J. Appl. Algebra Geom., 2023)

Generalized Ellipsoids. - Amir Ali Ahmadi; Abraar Chaudhry; Cemil Dibek (CoRR, 2024)

Robust-to-Dynamics Optimization. - Amir Ali Ahmadi; Oktay Günlük (Math. Oper. Res., 2025)