About

Amir Ali Ahmadi is a Professor of Operations Research and Financial Engineering at Princeton University, with affiliations across multiple departments and research centers including PACM, Computer Science, Mechanical & Aerospace Engineering, Electrical & Computer Engineering, the Center for Statistics and Machine Learning, Robotics, and the AI Lab. He serves as the Director of the Optimization and Quantitative Decision Science Minor. His academic background includes a Ph.D. in Electrical Engineering and Computer Science from MIT, where he was affiliated with the Laboratory for Information and Decision Systems, and his advisor was Prof. Pablo Parrilo. Prior to his current position, he was an Assistant Professor at Princeton, a Goldstine Fellow at IBM Watson Research Center, and a Visiting Research Scientist at Google Brain. He has also held roles such as Visiting Senior Optimization Fellow at Citadel GQS and Volunteer Assistant Coach for Princeton's Tennis Teams. His research focuses on optimization, control theory, and their applications in machine learning and data science, with notable contributions recognized through awards such as the Egon Balas Prize in Optimization, the Princeton Engineering Council Teaching Award, and the INFORMS Optimization Society Young Researchers' Prize. Ahmadi is actively involved in organizing conferences, seminars, and workshops, and has been featured in popular science articles explaining complex research topics to broader audiences.

Research topics

• Mathematical analysis
• Mathematics
• Mathematical optimization
• Applied mathematics
• Geometry
• Combinatorics

Selected publications

• Safely Learning Dynamical Systems

  Foundations of Computational Mathematics · 2025-02-04 · 2 citations

  article1st authorCorresponding
  PublisherDOI

• Convex Ternary Quartics Are SOS-Convex

  SIAM Journal on Optimization · 2025-08-26

  article1st authorCorresponding
  PublisherDOI

• Quantum Dynamics and Information Measures in PT and Anti-PT-Symmetric Systems

  ArXiv.org · 2025-08-05

  preprintOpen access1st authorCorresponding

  In this study, we investigate qubit dynamics under PT and Anti-PT-symmetric non-Hermitian Hamiltonians, focusing on phase evolution, decoherence, quantum speed limits (QSL), and Rényi entanglement entropies. Using similarity transformations and Dyson maps, we analyze the reduced density matrix evolution in bosonic environments. Anti-PT-symmetric systems show enhanced robustness against decoherence, with slower entropy growth and longer coherence times compared to PT-symmetric counterparts. QSL behavior is non-monotonic, reflecting rapid initial evolution followed by a gradual decrease. Higher-order Rényi entropies reveal that Anti-PT-symmetric qubits preserve quantum information more effectively, offering advantages for memory and cryptographic applications.

  PublisherOA PDFDOI

• Higher-order Newton methods with polynomial work per iteration

  Advances in Mathematics · 2024-07-03 · 4 citations

  article1st authorCorresponding
  PublisherDOI

• Convex Ternary Quartics Are SOS-Convex

  arXiv (Cornell University) · 2024-04-19

  preprintOpen access1st authorCorresponding

  We prove that convex ternary quartic forms are sum-of-squares-convex (sos-convex). This result is in a meaningful sense the ``convex analogue'' a celebrated theorem of Hilbert from 1888, where he proves that nonnegative ternary quartic forms are sums of squares. We show by an appropriate construction that exploiting the structure of the Hessian matrix is crucial in any possible proof of our result.

  PublisherOA PDFDOI

• Learning Dynamical Systems with Side Information

  SIAM Review · 2023-02-01 · 1 citations

  preprintOpen access1st authorCorresponding

  We present a mathematical and computational framework for learning a dynamical system from noisy observations of a few trajectories and subject to side information. Side information is any knowledge we might have about the dynamical system we would like to learn, besides trajectory data, and is typically inferred from domain-specific knowledge or basic principles of a scientific discipline. We are interested in explicitly integrating side information into the learning process in order to compensate for scarcity of trajectory observations. We identify six types of side information that arise naturally in many applications and lead to convex constraints in the learning problem. First, we show that when our model for the unknown dynamical system is parameterized as a polynomial, we can impose our side information constraints computationally via semidefinite programming. We then demonstrate the added value of side information for learning the dynamics of basic models in physics and cell biology, as well as for learning and controlling the dynamics of a model in epidemiology. Finally, we study how well polynomial dynamical systems can approximate continuously differentiable ones while satisfying side information (either exactly or approximately). Our overall learning methodology combines ideas from convex optimization, real algebra, dynamical systems, and functional approximation theory, and can potentially lead to new synergies among these areas.

  PublisherOA PDFDOI

• A Sum of Squares Characterization of Perfect Graphs

  SIAM Journal on Applied Algebra and Geometry · 2023-10-16 · 1 citations

  article1st authorCorresponding

  We present an algebraic characterization of perfect graphs, i.e., graphs for which the clique number and the chromatic number coincide for every induced subgraph. We show that a graph is perfect if and only if certain nonnegative polynomials associated with the graph are sums of squares. As a byproduct, we obtain several infinite families of nonnegative polynomials that are not sums of squares through graph-theoretic constructions. We also characterize graphs for which the associated polynomials belong to certain structured subsets of sum of squares polynomials. Finally, we reformulate some well-known results from the theory of perfect graphs as statements about sum of squares proofs of nonnegativity of certain polynomials.

  PublisherDOI

• Safely Learning Dynamical Systems

  arXiv (Cornell University) · 2023-05-20 · 1 citations

  preprintOpen access1st authorCorresponding

  A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. We formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize trajectories. The state of the system must stay within a safety region for a horizon of $T$ time steps under the action of all dynamical systems that (i) belong to a given initial uncertainty set, and (ii) are consistent with information gathered so far. First, we consider safely learning a linear dynamical system involving $n$ states. For the case $T=1$, we present an LP-based algorithm that either safely recovers the true dynamics from at most $n$ trajectories, or certifies that safe learning is impossible. For $T=2$, we give an SDP representation of the set of safe initial conditions and show that $\lceil n/2 \rceil$ trajectories generically suffice for safe learning. For $T = \infty$, we provide SDP-representable inner approximations of the set of safe initial conditions and show that one trajectory generically suffices for safe learning. We extend a number of our results to the cases where the initial uncertainty set contains sparse, low-rank, or permutation matrices, or when the system has a control input. Second, we consider safely learning a general class of nonlinear dynamical systems. For the case $T=1$, we give an SOCP-based representation of the set of safe initial conditions. For $T=\infty$, we provide semidefinite representable inner approximations to the set of safe initial conditions. We show how one can safely collect trajectories and fit a polynomial model of the nonlinear dynamics that is consistent with the initial uncertainty set and best agrees with the observations. We also present some extensions to cases where the measurements are noisy or the dynamical system involves disturbances.

  PublisherOA PDFDOI

• Higher-Order Newton Methods with Polynomial Work per Iteration

  arXiv (Cornell University) · 2023-11-10

  preprintOpen access1st authorCorresponding

  We present generalizations of Newton's method that incorporate derivatives of an arbitrary order $d$ but maintain a polynomial dependence on dimension in their cost per iteration. At each step, our $d^{\text{th}}$-order method uses semidefinite programming to construct and minimize a sum of squares-convex approximation to the $d^{\text{th}}$-order Taylor expansion of the function we wish to minimize. We prove that our $d^{\text{th}}$-order method has local convergence of order $d$. This results in lower oracle complexity compared to the classical Newton method. We show on numerical examples that basins of attraction around local minima can get larger as $d$ increases. Under additional assumptions, we present a modified algorithm, again with polynomial cost per iteration, which is globally convergent and has local convergence of order $d$.

  PublisherOA PDFDOI

• Review for "Study on the flow characteristics of the pulsating intermittent liquid‐solid fluidized bed with step liquid velocity by CFD approach"

  2022-02-09

  peer-review1st authorCorresponding
  PublisherDOI

Recent grants

• CAREER: Polynomial Optimization and Dynamical Systems

  NSF · $500k · 2016–2022

Frequent coauthors

• Pablo A. Parrilo

  39 shared

• Raphaël M. Jungers

  24 shared

• Mardavij Roozbehani

  Massachusetts Institute of Technology

  16 shared

• Anirudha Majumdar

  Princeton University

  14 shared

• Georgina Hall

  INSEAD

  11 shared

• Russ Tedrake

  9 shared

• Jeffrey Zhang

  7 shared

• Bachir El Khadir

  IBM Research - Thomas J. Watson Research Center

  7 shared

Labs

• Research GroupPI

Education

• Ph.D., Electrical Engineering and Computer Science

  Massachusetts Institute of Technology

  2011

• S.M., Electrical Engineering and Computer Science

  Massachusetts Institute of Technology

  2008

• B.S., Electrical Engineering

  University of Maryland, Baltimore

  2006

• B.S., Mathematics

  Massachusetts Institute of Technology

  2006

Awards & honors

• Egon Balas Prize in Optimization (2024)
• Excellence in Teaching Award of the Princeton Engineering Co…
• Distinguished Teaching Award of the Princeton School of Engi…
• Young Researchers' Prize of the INFORMS Optimization Society…
• 5-year Multidisciplinary University Research Initiative (MUR…