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

**Polynomial Root Radius Optimization with Affine Constraints**

Submitted for publication, May 2015.

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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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- 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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- 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

Published Article

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

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

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

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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

Published Article

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- 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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- 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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- 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: Proceedings of ROCOND 2003, Milan, June 2003

Postscript

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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.

Published Article

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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,

**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,

**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,

**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*****A good paper to read first***

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

**Differential Properties of the Spectral Abscissa and the Spectral Radius for Analytic Matrix-Valued Mappings**

*J. Nonl. Anal.: Theory, Methods, Appl.*23 (1994), pp. 467-488.

Postscript (final version sent to publisher)

Send e-mail for a reprint. - J.V. Burke and M.L. Overton,

**On the Subdifferentiability of Functions of a Matrix Spectrum**

I: Mathematical Foundations; II: Subdifferential Formulas

In: F. Giannessi (ed.),*Nonsmooth Optimization: Methods and Applications,*Gordon and Breach, Philadelphia, 1992, pp. 11-18 and 19-29.

I: Dvi (final version sent to publisher)

II: Dvi (final version sent to publisher)

Send e-mail for a reprint. - M.L. Overton and R.S. Womersley,

**On Minimizing the Spectral Radius of a Nonsymmetric Matrix Function - Optimality Conditions and Duality Theory**

*SIAM J. Matrix Anal. Appl.*9 (1988), pp. 473-498.

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E-mail address: overton@cs.nyu.edu

**Other Research Topics**