Research Output per year

## Research Output

## On Algebraic Proofs of Stability for Homogeneous Vector Fields

Ahmadi, A. A. & El Khadir, B., Jan 2020, In : IEEE Transactions on Automatic Control. 65, 1, p. 325-332 8 p., 8706528.Research output: Contribution to journal › Article

## On the complexity of detecting convexity over a box

Ahmadi, A. A. & Hall, G., Jul 1 2020, In : Mathematical Programming. 182, 1-2, p. 429-443 15 p.Research output: Contribution to journal › Article

## DSOS and SDSOS optimization: More tractable alternatives to sum of squares and semidefinite optimization

Ahmadi, A. A. & Majumdar, A., 2019, In : SIAM Journal on Applied Algebra and Geometry. 3, 2, p. 193-230 38 p.Research output: Contribution to journal › Article

## On the complexity of testing attainment of the optimal value in nonlinear optimization

Ahmadi, A. A. & Zhang, J., Jan 1 2019, In : Mathematical Programming.Research output: Contribution to journal › Article

## On the construction of converging hierarchies for polynomial optimization based on certificates of global positivity

Ahmadi, A. A. & Hall, G., 2019, In : Mathematics of Operations Research. 44, 4, p. 1192-1207 16 p.Research output: Contribution to journal › Article

## Polynomial norms

Ahmadi, A. A. L. I., Klerk, E. D. E. & Hall, G., 2019, In : SIAM Journal on Optimization. 29, 1, p. 399-422 24 p.Research output: Contribution to journal › Article

## A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function

Ahmadi, A. A. & El Khadir, B., Nov 2018, In : Systems and Control Letters. 121, p. 50-53 4 p.Research output: Contribution to journal › Article

## DC decomposition of nonconvex polynomials with algebraic techniques

Ahmadi, A. A. & Hall, G., May 1 2018, In : Mathematical Programming. 169, 1, p. 69-94 26 p.Research output: Contribution to journal › Article

## Improving efficiency and scalability of sum of squares optimization: Recent advances and limitations

Ahmadi, A. A., Hall, G., Papachristodoulou, A., Saunderson, J. & Zheng, Y., Jan 18 2018,*2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017.*Institute of Electrical and Electronics Engineers Inc., p. 453-462 10 p. (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

Jungers, R. M., Ahmadi, A. A., Parrilo, P. A. & Roozbehani, M., Jun 1 2017, In : IEEE Transactions on Automatic Control. 62, 6, p. 3062-3067 6 p., 7858590.Research output: Contribution to journal › Article

## Geometry of 3D environments and sum of squares polynomials

Ahmadi, A. A., Hall, G., Makadia, A. & Sindhwani, V., Jan 1 2017,*Robotics: Science and Systems XIII, RSS 2017.*Srinivasa, S., Ayanian, N., Amato, N. & Kuindersma, S. (eds.). MIT Press Journals, (Robotics: Science and Systems; vol. 13).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Optimization over structured subsets of positive semidefinite matrices via column generation

Ahmadi, A. A., Dash, S. & Hall, G., May 1 2017, In : Discrete Optimization. 24, p. 129-151 23 p.Research output: Contribution to journal › Article

## Some recent directions in algebraic methods for optimization and lyapunov analysis

Ahmadi, A. A. & Parrilo, P. A., 2017,*Springer Tracts in Advanced Robotics.*Springer Verlag, p. 89-112 24 p. (Springer Tracts in Advanced Robotics; vol. 117).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

## Sum of squares basis pursuit with linear and second order cone programming

Ahmadi, A. A. & Hall, G., 2017,*Contemporary Mathematics.*American Mathematical Society, p. 27-53 27 p. (Contemporary Mathematics; vol. 685).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

Ahmadi, A. A. & Parrilo, P. A., Oct 1 2017, In : IEEE Transactions on Automatic Control. 62, 10, p. 5269-5274 6 p., 7803555.Research output: Contribution to journal › Article

## Lower bounds on complexity of Lyapunov functions for switched linear systems

Ahmadi, A. A. & Jungers, R. M., Aug 1 2016, In : Nonlinear Analysis: Hybrid Systems. 21, p. 118-129 12 p.Research output: Contribution to journal › Article

## Some applications of polynomial optimization in operations research and real-time decision making

Ahmadi, A. A. & Majumdar, A., Apr 1 2016, In : Optimization Letters. 10, 4, p. 709-729 21 p.Research output: Contribution to journal › Article

## Robust-to-dynamics linear programming

Ahmadi, A. A. & Günluk, O., Feb 8 2015,*54rd IEEE Conference on Decision and Control,CDC 2015.*Institute of Electrical and Electronics Engineers Inc., p. 5915-5919 5 p. 7403149. (Proceedings of the IEEE Conference on Decision and Control; vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Control and verification of high-dimensional systems with DSOS and SDSOS programming

Majumdar, A., Ahmadi, A. A. & Tedrake, R., Jan 1 2014, In : Proceedings of the IEEE Conference on Decision and Control. 2015-February, February, p. 394-401 8 p., 7039413.Research output: Contribution to journal › Conference article

## DSOS and SDSOS optimization: LP and SOCP-based alternatives to sum of squares optimization

Ahmadi, A. A. & Majumdar, A., Jan 1 2014.Research output: Contribution to conference › Paper

## Joint spectral radius and path-complete graph Lyapunov functions

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., Mar 28 2014, In : SIAM Journal on Control and Optimization. 52, 1, p. 687-717 31 p.Research output: Contribution to journal › Article

## On complexity of Lyapunov functions for switched linear systems

Ahmadi, A. A. & Jungers, R. M., 2014,*19th IFAC World Congress IFAC 2014, Proceedings.*Boje, E. & Xia, X. (eds.). IFAC Secretariat, p. 5992-5997 6 p. (IFAC Proceedings Volumes (IFAC-PapersOnline); vol. 19).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Towards scalable algorithms with formal guarantees for Lyapunov analysis of control systems via algebraic optimization

Ahmadi, A. A. & Parrilo, P. A., Jan 1 2014, In : Proceedings of the IEEE Conference on Decision and Control. 2015-February, February, p. 2272-2281 10 p., 7039734.Research output: Contribution to journal › Conference article

## A complete characterization of the gap between convexity and sos-convexity

Ahmadi, A. A. & Parrilo, P. A., Aug 1 2013, In : SIAM Journal on Optimization. 23, 2, p. 811-833 23 p.Research output: Contribution to journal › Article

## Complexity of ten decision problems in continuous time dynamical systems

Ahmadi, A. A., Majumdar, A. & Tedrake, R., 2013,*2013 American Control Conference, ACC 2013.*Institute of Electrical and Electronics Engineers Inc., p. 6376-6381 6 p. 6580838. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Control design along trajectories with sums of squares programming

Majumdar, A., Ahmadi, A. A. & Tedrake, R., Nov 14 2013,*2013 IEEE International Conference on Robotics and Automation, ICRA 2013.*p. 4054-4061 8 p. 6631149. (Proceedings - IEEE International Conference on Robotics and Automation).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## NP-hardness of deciding convexity of quartic polynomials and related problems

Ahmadi, A. A., Olshevsky, A., Parrilo, P. A. & Tsitsiklis, J. N., 2013, In : Mathematical Programming. 137, 1-2, p. 453-476 24 p.Research output: Contribution to journal › Article

## Switched stability of nonlinear systems via SOS-convex Lyapunov functions and semidefinite programming

Ahmadi, A. A. & Jungers, R. M., Jan 1 2013,*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013.*Institute of Electrical and Electronics Engineers Inc., p. 727-732 6 p. 6759968. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## A convex polynomial that is not sos-convex

Ahmadi, A. A. & Parrilo, P. A., Oct 1 2012, In : Mathematical Programming. 135, 1-2, p. 275-292 18 p.Research output: Contribution to journal › Article

## Feasibility checks and control laws for reconfigurations of spacecraft clusters

Moshtagh, N., Ahmadi, A. A. & Mesbahi, M., Jan 1 2012,*2012 American Control Conference, ACC 2012.*Institute of Electrical and Electronics Engineers Inc., p. 961-966 6 p. 6315644. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Joint spectral radius of rank one matrices and the maximum cycle mean problem

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2012, In : Proceedings of the IEEE Conference on Decision and Control. p. 731-733 3 p., 6425992.Research output: Contribution to journal › Conference article

## On the difficulty of deciding asymptotic stability of cubic homogeneous vector fields

Ahmadi, A. A., Nov 26 2012,*2012 American Control Conference, ACC 2012.*p. 3334-3339 6 p. 6315687. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## When is a set of LMIs a sufficient condition for stability

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., Sep 17 2012,*ROCOND'12 - 7th IFAC Symposium on Robust Control Design.*PART 1 ed. p. 313-318 6 p. (IFAC Proceedings Volumes (IFAC-PapersOnline); vol. 7, no. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## A globally asymptotically stable polynomial vector field with no polynomial Lyapunov function

Ahmadi, A. A., Krstic, M. & Parrilo, P. A., Dec 1 2011,*2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011.*p. 7579-7580 2 p. 6161499. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Analysis of the joint spectral radius via Lyapunov functions on path-complete graphs

Ahmadi, A. A., Jungers, R. M., Parrilo, P. A. & Roozbehani, M., May 20 2011,*HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control.*p. 13-22 10 p. (HSCC'11 - Proceedings of the 2011 ACM/SIGBED Hybrid Systems: Computation and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Converse results on existence of sum of squares Lyapunov functions

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2011,*2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011.*p. 6516-6521 6 p. 6161493. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## On higher order derivatives of Lyapunov functions

Ahmadi, A. A. & Parrilo, P. A., Sep 29 2011,*Proceedings of the 2011 American Control Conference, ACC 2011.*p. 1313-1314 2 p. 5991573. (Proceedings of the American Control Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## On the equivalence of algebraic conditions for convexity and quasiconvexity of polynomials

Ali Ahmadi, A. & Parrilo, P. A., Dec 1 2010,*2010 49th IEEE Conference on Decision and Control, CDC 2010.*p. 3343-3348 6 p. 5717510. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Piecewise polynomial Lyapunov functions with guaranteed accuracy

Ahmadi, A. A., Jungers, R. M., Parrilo, P. & Roozbehani, M., Dec 1 2010,*2010 IEEE 26th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2010.*1 p. 5662189. (2010 IEEE 26th Convention of Electrical and Electronics Engineers in Israel, IEEEI 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## A positive definite polynomial Hessian that does not factor

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2009,*Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009.*p. 1195-1200 6 p. 5400519. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Non-monotonic Lyapunov functions for stability of discrete time nonlinear and switched systems

Ahmadi, A. A. & Parrilo, P. A., Dec 1 2008,*Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008.*p. 614-621 8 p. 4739402. (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## High-speed broadband polarization-independent optical clock recovery in a silicon detector

Ahmadi, A. A., Salem, R. & Murphy, T. E., Dec 14 2006,*Proceedings - Thirteenth International Symposium on Temporal Representation and Reasoning, TIME 2006.*Vol. 2006. 1636694

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

## Two-photon absorption for optical clock recovery in OTDM networks

Salem, R., Ahmadi, A. A., Tudury, G. E., Carter, G. M. & Murphy, T. E., Sep 1 2006, In : Journal of Lightwave Technology. 24, 9, p. 3353-3361 9 p.Research output: Contribution to journal › Article