Optimization of Eigenvalues of Nonsymmetric Matrices and Roots of Polynomials

• O.N. Kirillov and M.L. Overton,
  Finding the Strongest Stable Massless Column with a Follower Load and Relocatable Concentrated Masses
  Quart. J. Mech. Appl. Math. 74 (2021), pp. 223-250
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• J. Eaton, S. Grundel, M. Gürbüzbalaban and M.L. Overton,
  Polynomial Root Radius Optimization with Affine Constraints
  Math. Programming 165 (2017), pp. 509–528
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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
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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
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• 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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• 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.
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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)
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• 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)
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• 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.
  Copy of Published Article (pdf)
  

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