- A. Greenbaum and M.L. Overton,

**Numerical Investigation of Crouzeix's Conjecture**

Submitted to Linear Algebra Applications, 2016.

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- A. Greenbaum, A.S. Lewis and M.L. Overton,

**Variational Analysis of the Crouzeix Ratio**

To appear in Math. Programming, 2016.

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- F.E. Curtis, T. Mitchell and M.L. Overton,

**A BFGS-SQP Method for Nonsmooth, Nonconvex, Constrained Optimization and its Evaluation using Relative Minimization Profiles**

Optimization Methods and Software, 2016

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- T. Mitchell and M.L. Overton,

**Fixed Low-Order Controller Design and H**_{∞}Optimization for Large-Scale Dynamical Systems

In: Proceedings of 8th IFAC Symposium on Robust Control Design, Bratislava, 8-11 July 2015 (ROCOND 2015), pp. 25-30

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- J. Eaton, S. Grundel, M. Gürbüzbalaban and M.L. Overton,

**Polynomial Stabilization with Bounds on the Controller Coefficients**

In: Proceedings of 8th IFAC Symposium on Robust Control Design, Bratislava, 8-11 July 2015 (ROCOND 2015), pp. 381-386

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- J. Eaton, S. Grundel, M. Gürbüzbalaban and M.L. Overton,

**Polynomial Root Radius Optimization with Affine Constraints**

Submitted for publication, 2015.

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- T. Mitchell and M.L. Overton,

**Hybrid Expansion-Contraction: a Robust Scaleable Method for Approximating the H**_{∞}Norm

IMA J. Numer. Anal., 2015, doi: 10.1093/imanum/drv046

Published Article

- N. Guglielmi, M.L. Overton and G.W. Stewart,

**An Efficient Algorithm for Computing the Generalized Null Space Decomposition**

SIAM J. Matrix Anal. Appl. 36 (2015), pp. 38-54

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- I. M. Bomze and M.L. Overton,

**Narrowing the Difficulty Gap for the Celis-Dennis-Tapia Problem**

Math. Programming 151 (2015), pp. 459-476

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- O. Kirillov and M.L. Overton,

**Robust Stability at the Swallowtail Singularity**

Frontiers in Mathematical Physics 1 (2013), Article 24, doi: 10.3389/fphy.2013.00024

Published Article

- M.L. Overton,

**Stability Optimization for Polynomials and Matrices**

In: Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations (O. Kirillov and D. Pelinovsky, eds.), Wiley, 2014, pp. 351-375.

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- N. Guglielmi, M. Gürbüzbalaban and M.L. Overton,

**Fast Approximation of the H**_{∞}Norm via Optimization over Spectral Value Sets

SIAM J. Matrix Anal. Appl. 34 (2013), pp. 709-737

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- S. Grundel and M.L. Overton,

**Variational Analysis of the Spectral Abscissa at a Matrix with a Nongeneric Multiple Eigenvalue**

Set-Valued and Variational Analysis 22 (2014), pp. 19-43

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- C. Helmberg, F. Rendl and M.L. Overton,

**The Spectral Bundle Method with Second-Order Information**

Optimization Methods and Software 29 (2014), pp. 855-876

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- A.S. Lewis and M.L. Overton,

**Nonsmooth Optimization via Quasi-Newton Methods**

Math. Programming 141 (2013), pp. 135-163

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- V.D. Blondel, M. Gürbüzbalaban, A. Megretski and M.L. Overton,

**Explicit Solutions for Root Optimization of a Polynomial Family with One Affine Constraint**

IEEE Trans. Auto. Control 57 (2012), pp. 3078 - 3089

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- F.E. Curtis and M.L. Overton,

**A Sequential Quadratic Programming Algorithm for Nonconvex, Nonsmooth Constrained Optimization**

SIAM J. Optimization 22 (2012), pp. 474-500

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- M. Gürbüzbalaban and M.L. Overton,

**Some Regularity Results for the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix**

SIAM J. Optimization 22 (2012), pp. 281-285

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- M. Gürbüzbalaban and M.L. Overton,

**On Nesterov's Nonsmooth Chebyshev-Rosenbrock Functions**

*Nonlinear Analysis: Theory, Methods and Applications*75 (2012), pp. 1282-1289

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- N. Guglielmi and M.L. Overton,

**Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix**

SIAM J. Matrix Anal. Appl. 32 (2011), pp. 1166-1192

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- V.D. Blondel, M. Gürbüzbalaban, A. Megretski and M.L. Overton,

**Explicit Solutions for Root Optimization of a Polynomial Family**

Proceedings of the 49th IEEE Conference on Decision and Control (CDC 2010)

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- C. Greif and M.L. Overton,

**An Analysis of Low-Rank Modifications of Preconditioners for Saddle Point Systems**

*Elec. Trans. Numer. Anal.*37 (2010), pp. 307-320

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- Z. Deng, M. Gu and M.L. Overton,

**Structured Primal-Dual Interior-Point Methods for Banded Semidefinite Programming**

*Operator Theory: Advances and Applications*202 (2009), pp. 111-141. - R. Alam, S. Bora, R. Byers and M.L. Overton,

**Characterization and Construction of the Nearest Defective Matrix via Coalescence of Pseudospectral Components**

*Linear Algebra and its Applications*435 (2011), pp. 494-513

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- A.S. Lewis and M.L. Overton,

**Nonsmooth Optimization via BFGS**

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- A.S. Lewis and M.L. Overton,

**Behavior of BFGS with an Exact Line Search on Nonsmooth Examples**

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- S. Gumussoy, D. Henrion, M. Millstone and M.L. Overton,

**Multiobjective Robust Control with HIFOO 2.0**

In: Proceedings of 6th IFAC Symposium on Robust Control Design, Haifa, 16-18 June 2009 (ROCOND 2009)

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- S. Gumussoy, M. Millstone and M.L. Overton,

**H-infinity Strong Stabilization via HIFOO, a Package for Fixed-Order Controller Design**

In: Proceedings of 47th IEEE Conference on Decision and Control (CDC 2008), Cancun, 9-11 Dec. 2008, pp. 4135 - 4140

PDF - S. Gumussoy and M.L. Overton,

**Fixed-Order H-infinity Controller Design via HIFOO, a Specialized Nonsmooth Optimization Package**

In: Proceedings of American Control Conference, 2008 (ACC 2008), Seattle, 11-13 June 2008 (ACC 2008) pp. 2750-2754

PDF - J.V. Burke, A.S. Lewis and M.L. Overton,

**The Speed of Shor's R-Algorithm**

*IMA J. Numer. Anal.*28 (2008), pp. 711-720

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Spectral Conditioning and Pseudospectral Growth**

*Numerische Mathematik*107 (2007), pp. 27-37

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Copy of Published Article (pdf) - J.V. Burke, A.S. Lewis and M.L. Overton,

**Convexity and Lipschitz Behavior of Small Pseudospectra**

*SIAM J. Matrix Anal. Appl.*29 (2007), pp. 586-595

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- M. Fukuda, B.J. Braams, M. Nakata, M.L. Overton, J.K. Percus, M. Yamashita and Z. Zhao

**Large-Scale Semidefinite Programs in Electronic Structure Calculation**

*Math. Programming*109 (2007), pp. 553-580.

Published Article

Copy of Published Article (pdf) - K. K. Gade and M.L. Overton,

**Optimizing the Asymptotic Convergence Rate of the Diaconis-Holmes-Neal Sampler**

*Advances in Applied Mathematics*38 (2007) pp. 382-403

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- D. Henrion and M.L. Overton,

**Maximizing the Closed Loop Asymptotic Decay Rate for the Two-Mass-Spring Control Problem**

PDF - J.V. Burke, D. Henrion, A.S. Lewis and M.L. Overton,

**Stabilization via Nonsmooth, Nonconvex Optimization**

*IEEE Transactions on Automatic Control*51 (2006) pp. 1760-1769

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- M. Gu, E. Mengi, M.L. Overton, J. Xia and J. Zhu,

**Fast Methods for Estimating the Distance to Uncontrollability**

*SIAM J. Matrix Anal. Appl.*28 (2006), pp. 477-502

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- M. Gu and M.L. Overton,

**An Algorithm to Compute Sep_Lambda**

*SIAM J. Matrix Anal. Appl.*28 (2006), pp. 348-359.

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- J.V. Burke, D. Henrion, A.S. Lewis and M.L. Overton,

**HIFOO - A MATLAB Package for Fixed-Order Controller Design and H-infinity Optimization**

In: Proceedings of 5th IFAC Symposium on Robust Control Design, Toulouse, July 2006 (ROCOND 2006)

PDF - M.L. Overton and P. Van Dooren,

**On Computing the Complex Passivity Radius**

In: Proceedings of CDC-ECC 05, Sevilla, Dec 2005

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Bibliographic Update

- E. Mengi and M.L. Overton,

**Algorithms for the Computation of the Pseudospectral Radius and the Numerical Radius of a Matrix**

*IMA Journal of Numerical Analysis*25 (2005) pp. 648-669.

Published Article

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization**

*SIAM J. Optimization*15 (2005), pp. 751-779.

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Problem Data and Software

- J.V. Burke, A.S. Lewis and M.L. Overton,

**Variational Analysis of Functions of the Roots of Polynomials**

*Math Programming*104 (2005), pp. 263-292.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Pseudospectral Components and the Distance to Uncontrollability**

*SIAM J. Matrix Anal. Appl.*26 (2004), pp. 350-361.

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- Z. Zhao, B.J. Braams, M. Fukuda, M.L. Overton and J.K. Percus

**The Reduced Density Matrix Method for Electronic Structure Calculations and the Role of Three-Index Representability**

*Journal of Chemical Physics*120 (2004), pp. 2095-2104.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by Static Output Feedback and Low-Order Controllers**

In: S.Bittanti and P. Colaneri, eds., Proceedings of 4th IFAC Symposium on Robust Control Design, Milan, June 2003 (ROCOND 2003), pp. 175-181 (Elsevier, 2004)

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Individual figures and problem data

- J.V. Burke, A.S. Lewis and M.L. Overton,

**Variational Analysis of the Abscissa Mapping for Polynomials via the Gauss-Lucas Theorem**

*Journal of Global Optimization*28 (2004), pp. 259-268.

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- B. Han, M.L. Overton and T. P.-Y. Yu,

**Design of Hermite Subdivision Schemes Aided by Spectral Radius Optimization**

*SIAM J. Scient. Comp.*25 (2003), pp. 643-656.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Robust Stability and A Criss-Cross Algorithm for Pseudospectra**

*IMA Journal of Numerical Analysis*23 (2003), pp. 359-375.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Optimization and Pseudospectra, with Applications to Robust Stability**

*SIAM J. Matrix Anal. Appl.*25 (2003), pp. 80-104.

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Corrigendum

- J.V. Burke, A.S. Lewis and M.L. Overton,

**Approximating Subdifferentials by Random Sampling of Gradients**

*Mathematics of Operations Research*27 (2002), pp. 567-584.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Two Numerical Methods for Optimizing Matrix Stability**

*Linear Algebra and its Applications*351-352 (2002), pp. 117-145.

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Other Supporting Files

- J.V. Burke, A.S. Lewis and M.L. Overton,

**Optimal Stability and Eigenvalue Multiplicity**

*Foundations of Computational Mathematics*1 (2001), pp. 205-225.

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- J.V. Burke, A.S. Lewis and M.L. Overton,

**Optimizing Matrix Stability***Proceedings of the American Mathematical Society*129 (2001), pp. 1635-1642.

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- J.V. Burke and M.L. Overton,

**Variational Analysis of the Abscissa Mapping for Polynomials**

*SIAM J. Control Optim.*39 (2001), pp. 1651-1676.

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- J.V. Burke and M.L. Overton,

**Variational Analysis of Non-Lipschitz Spectral Functions**

*Math. Programming*90 (2001), pp. 317-351.

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- K.D. Andersen, E. Christiansen, A.R. Conn and M.L. Overton,

**An Efficient Primal-Dual Interior-Point Method for Minimizing a Sum of Euclidean Norms**

*SIAM J. Scient. Comp.*22 (2000), pp. 243-262.

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**List of Papers by Research Topics**