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Associate Professor Robert Womersley

Associate Professor Robert Womersley

Honorary Associate Professor

PhD, MSc University of Dundee, BSc (Hons) Adelaide University

Science
School of Mathematics & Statistics

I was a staff member of the School of Mathematics and Statistics from 1985 to 2015, and an honorary since then.

I have held visiting/short term positions at Vanderbilt University, ICERM, Hong Kong Polytechnic University, Argonne National Laboratory, Courant Institute, Australian National University and University of Kentucky.

Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 1037
  • Books | 1997
    1997, Computational nonsmooth optimization, Qi L; Ruszczynski A; Womersley RS, (eds.), Mathematical Programming Society, North Holland
    Books | 1995
    Du D-Z; Qi L; Womersley RS, 1995, Recent Advances in Nonsmooth Optimization, WORLD SCIENTIFIC,
  • Book Chapters | 2018
    Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2018, 'Logarithmic and riesz equilibrium for multiple sources on the sphere: The exceptional case', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 179 - 203,
    Book Chapters | 2015
    Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35,
    Book Chapters | 2015
    Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical integration on the sphere', in Handbook of Geomathematics: Second Edition, Springer Nature, pp. 2671 - 2710,
    Book Chapters | 2013
    Hesse K; Sloan IH; Womersley RS, 2013, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1 - 35,
    Book Chapters | 2010
    Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Handbook of Geomathematics, Springer Berlin Heidelberg, pp. 1185 - 1219,
    Book Chapters | 2010
    Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Freeden W; Nashed MZ; Sonar T (ed.), Handbook of Geomathematics, Springer, Berlin, pp. 1187 - 1220
  • Journal articles | 2024
    Brauchart JS; Grabner PJ; Sloan IH; Womersley RS, 2024, 'Needlets liberated', Applied and Computational Harmonic Analysis, 73,
    Journal articles | 2024
    Hamann J; Le Gia QT; Sloan IH; Womersley RS, 2024, 'Removing the Mask—Reconstructing a Real-Valued Field on the Sphere from a Masked Field by Spherical Fourier Analysis', SIAM Journal on Imaging Sciences, 17, pp. 1820 - 1843,
    Journal articles | 2023
    Chafaï D; Saff EB; Womersley RS, 2023, 'Threshold condensation to singular support for a Riesz equilibrium problem', Analysis and Mathematical Physics, 13,
    Journal articles | 2023
    Wang YG; Womersley RS; Wu HT; Yu WH, 2023, 'Numerical computation of triangular complex spherical designs with small mesh ratio', Journal of Computational and Applied Mathematics, 421, pp. 114796 - 114796,
    Journal articles | 2022
    Chafaï D; Saff EB; Womersley RS, 2022, 'On the solution of a Riesz equilibrium problem and integral identities for special functions', Journal of Mathematical Analysis and Applications, 515,
    Journal articles | 2021
    Hamann J; Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2021, 'A new probe of Gaussianity and isotropy with application to cosmic microwave background maps', International Journal of Modern Physics C, 32,
    Journal articles | 2021
    Hesse K; Sloan IH; Womersley RS, 2021, 'Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data', Journal of Computational and Applied Mathematics, 382,
    Journal articles | 2021
    Sourisseau M; Wang YG; Womersley RS; Wu HT; Yu WH, 2021, 'Improve concentration of frequency and time (ConceFT) by novel complex spherical designs', Applied and Computational Harmonic Analysis, 54, pp. 137 - 144,
    Journal articles | 2020
    Sourisseau M; Wang YG; Womersley RS; Wu H-T; Yu W-H, 2020, 'Improve Concentration of Frequency and Time (Conceft) by Novel Complex Spherical Designs', ,
    Journal articles | 2019
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2019, 'Isotropic sparse regularization for spherical harmonic representations of random fields on the sphere', Applied and Computational Harmonic Analysis,
    Journal articles | 2019
    Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, 'Numerical computation of triangular complex spherical designs with small mesh ratio', ,
    Journal articles | 2018
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere-Hole Radii, Covering, and Separation', EXPERIMENTAL MATHEMATICS, 27, pp. 62 - 81,
    Journal articles | 2018
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81,
    Journal articles | 2018
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81,
    Journal articles | 2018
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2018, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 62 - 81,
    Journal articles | 2018
    Chen X; Womersley RS, 2018, 'Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere', SIAM Journal on Imaging Sciences, 11, pp. 1390 - 1415,
    Journal articles | 2018
    Womersley RS, 2018, 'Efficient spherical designs with good geometric properties', , pp. 1243 - 1285,
    Journal articles | 2017
    Hesse K; Sloan IH; Womersley RS, 2017, 'Radial basis function approximation of noisy scattered data on the sphere', Numerische Mathematik, 137, pp. 579 - 605,
    Journal articles | 2017
    Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, 216, pp. 86 - 116,
    Journal articles | 2017
    Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, 43, pp. 292 - 316,
    Journal articles | 2016
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2016, 'Random Point Sets on the Sphere—Hole Radii, Covering, and Separation', Experimental Mathematics, 27, pp. 1 - 20,
    Journal articles | 2016
    Wang YG; Sloan IH; Womersley RS, 2016, 'Riemann Localisation on the Sphere', Journal of Fourier Analysis and Applications, 24, pp. 1 - 43,
    Journal articles | 2015
    Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces', Journal of Mathematical Analysis and Applications, 431, pp. 782 - 811,
    Journal articles | 2015
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, 'Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation', ,
    Journal articles | 2014
    An C; Chen X; Sloan IH; Womersley RS, 2014, 'Erratum: Regularized least squares approximations on the sphere using spherical designs (SIAM Journal on Numerical Analysis (2012) 50 (1513-1534))', SIAM Journal on Numerical Analysis, 52, pp. 2205 - 2206,
    Journal articles | 2014
    Brauchart JS; Saff EB; Sloan IH; Womersley RS, 2014, 'QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere', Mathematics of Computation, 83, pp. 2821 - 2851,
    Journal articles | 2014
    Chernih A; Sloan IH; Womersley RS, 2014, 'Wendland functions with increasing smoothness converge to a Gaussian', Advances in Computational Mathematics, 40, pp. 185 - 200,
    Journal articles | 2012
    An C; Chen X; Sloan IH; Womersley RS, 2012, 'Regularized least squares approximations on the sphere using spherical designs', SIAM Journal on Numerical Analysis, 50, pp. 1513 - 1534,
    Journal articles | 2012
    Hesse K; Womersley RS, 2012, 'Numerical integration with polynomial exactness over a spherical cap', Advances in Computational Mathematics, 36, pp. 451 - 483,
    Journal articles | 2012
    Sloan IH; Womersley RS, 2012, 'Filtered hyperinterpolation: a constructive polynomial approximation on the sphere', International Journal on Geomathematics, 3, pp. 95 - 117,
    Journal articles | 2011
    Chen X; Womersley RS; Ye JJ, 2011, 'Minimizing the condition number of a gram matrix', SIAM Journal on Optimization, 21, pp. 127 - 148,
    Journal articles | 2010
    An C; Chen X; Sloan IH; Womersley RS, 2010, 'Well conditioned spherical designs for integration and interpolation on the two-sphere', SIAM Journal on Numerical Analysis, 48, pp. 2135 - 2157,
    Journal articles | 2009
    Sloan IH; Womersley RS, 2009, 'A variational characterisation of spherical designs', Journal of Approximation Theory, 159, pp. 308 - 318
    Journal articles | 2008
    Evans JR; Womersley RS; Wong D; Woodbury G, 2008, 'Operational Risk in Banks', JASSA - Journal of the Securities Institute of Australia, 2, pp. 9 - 16
    Journal articles | 2008
    Kuo FY; Dunsmuir WT; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, 10, pp. 239 - 275
    Journal articles | 2008
    Leopardi PC; Womersley RS, 2008, 'Porting a sphere optimization program from LAPACK to ScaLAPACK', The ANZIAM Journal, 50, pp. C204 - C219
    Journal articles | 2008
    Polak E; Womersley RS; Yin H, 2008, 'An algorithm based on active sets and smoothing for discretized semi-infinile minimax problems', Journal of Optimization Theory and Applications
    Journal articles | 2006
    Chen X; Womersley RS, 2006, 'Existence of solutions to systems of underdetermined equations and spherical designs', SIAM Journal on Numerical Analysis, 44, pp. 2326 - 2341
    Journal articles | 2006
    Jeyakumar V; Ormerod JT; Womersley RS, 2006, 'Knowledge-based semidefinite linear programming classifiers', Optimization Methods and Software, 21, pp. 693 - 706,
    Journal articles | 2004
    Sloan IH; Womersley RS, 2004, 'Extremal systems of points and numerical integration on the sphere', Advances in Computational Mathematics, 21, pp. 107 - 125
    Journal articles | 2003
    Polak E; Royset JO; Womersley RS, 2003, 'Algorithms with adaptive smoothing for finite minimax problems', Journal of Optimization Theory and Applications, 119, pp. 459 - 484
    Journal articles | 2002
    Sloan IH; Womersley RS, 2002, 'Good approximation on the sphere, with application to geodesy and the scattering of sound', Journal of Computational and Applied Mathematics, 149, pp. 227 - 237
    Journal articles | 2002
    Sun D; Womersley RS; Qi H, 2002, 'A feasible semismooth asymptotically Newton method for mixed complementarity problems', Mathematical Programming, 94, pp. 167 - 187
    Journal articles | 2001
    Gonsalkorale K; Womersley RS, 2001, 'Multistage quadratic stochastic programming', Journal of Computational and Applied Mathematics, 129, pp. 105 - 138
    Journal articles | 2001
    Womersley RS; Sloan IH, 2001, 'How good can polynomial interpolation on the sphere be?', Advances in Computational Mathematics, 14, pp. 195 - 226
    Journal articles | 2000
    Chen X; Womersley RS, 2000, 'Random test problems and parallel methods for quadratic programs and quadratic stochastic programs', Optimization Methods and Software, 13, pp. 275 - 306,
    Journal articles | 2000
    Sloan IH; Womersley RS, 2000, 'Constructive polynomial approximation on the sphere', Journal of Approximation Theory, 103, pp. 91 - 118
    Journal articles | 2000
    Womersley RS, 2000, 'A continuous minimax problem for calculating minimum norm polynomial interpolation points on the sphere ANZIAM journal', Journal of Australian Mathematical Society B, pp. 1536 - 1557
    Journal articles | 1999
    Sun D; Womersley RS, 1999, 'A new unconstrained differentiable merit function for box constrained variational inequality problems and a damped Gauss-Newton method', SIAM Journal on Optimization, 9, pp. 388 - 413,
    Journal articles | 1998
    Chen X; Womersley RS, 1998, 'Stochastic programming', New South Wales Centre for Parallel Computine, pp. 10 - 10
    Journal articles | 1998
    Khoury F; Standish RK; Womersley RS, 1998, 'Parallel triangular system solvers', New South Wales Centre for Parallel Computine, pp. 21 - 22
    Journal articles | 1996
    Qi L; Womersley RS, 1996, 'On extreme singular values of matrix valued functions', Journal of Convex Analysis, 3, pp. 153 - 166
    Journal articles | 1996
    Tin Loi FS; Qi L; Wei Z; Womersley RS, 1996, 'Stochastic ultimate load analysis: models and solution methods', Numerical Functional Analysis and Optimization, 17, pp. 1029 - 1043
    Journal articles | 1995
    Chen X; Qi L; Womersley RS, 1995, 'Newton's method for quadratic stochastic programs with recourse', Journal of Computational and Applied Mathematics, 60, pp. 29 - 46,
    Journal articles | 1995
    Overton ML; Womersley RS, 1995, 'Second derivatives for optimizing eigenvalues of symmetric matrices', SIAM Journal on Matrix Analysis and Applications, 16, pp. 697 - 718
    Journal articles | 1995
    Qi L; Womersley RS, 1995, 'An SQP algorithm for extended linear-quadratic problems in stochastic programming', Annals of Operations Research, pp. 251 - 285
    Journal articles | 1993
    Overton ML; Womersley RS, 1993, 'Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices', Mathematical Programming, 62, pp. 321 - 357,
    Journal articles | 1992
    Overton ML; Womersley RS, 1992, 'On the Sum of the Largest Eigenvalues of a Symmetric Matrix', SIAM Journal on Matrix Analysis and Applications, 13, pp. 41 - 45,
    Journal articles | 1990
    Osborne MR; Womersley RS, 1990, 'Strong uniqueness in sequential linear programming', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 31, pp. 379 - 384,
    Journal articles | 1988
    Overton ML; Womersley RS, 1988, 'On Minimizing the Special Radius of a Nonsymmetric Matrix Function: Optimality Conditions and Duality Theory', SIAM Journal on Matrix Analysis and Applications, 9, pp. 473 - 498,
    Journal articles | 1986
    Osborne MR; Pruess SA; Womersley RS, 1986, 'Concise representation of generalised gradients', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 28, pp. 57 - 74,
    Journal articles | 1986
    Womersley RS; Fletcher R, 1986, 'An algorithm for composite nonsmooth optimization problems', Journal of Optimization Theory and Applications, 48, pp. 493 - 523,
    Journal articles | 1986
    Womersley RS, 1986, 'Censored Discrete Linear $l_1 $ Approximation', SIAM Journal on Scientific and Statistical Computing, 7, pp. 105 - 122,
    Journal articles | 1985
    Womersley RS, 1985, 'Local properties of algorithms for minimizing nonsmooth composite functions', Mathematical Programming, 32, pp. 69 - 89,
    Journal articles | 1983
    Teo KL, 1983, 'A Control Parametrization Algorithm for Optimal Control Problems Involving Linear Systems and Linear Terminal Inequality Constraints', Numerical Functional Analysis and Optimization, 6, pp. 291 - 313,
  • Working Papers | 2019
    Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps, ,
    Working Papers | 2018
    Gia QTL; Sloan IH; Womersley RS; Wang YG; Le Gia Q, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere,
  • Preprints | 2023
    Hamann J; Gia QTL; Sloan IH; Womersley RS, 2023, Removing the mask -- reconstructing a scalar field on the sphere from a masked field,
    Preprints | 2022
    Brauchart JS; Grabner PJ; Sloan IH; Womersley RS, 2022, Needlets Liberated,
    Preprints | 2022
    Chafaï D; Saff EB; Womersley RS, 2022, Threshold condensation to singular support for a Riesz equilibrium problem, ,
    Preprints | 2021
    Chafaï D; Saff EB; Womersley RS, 2021, On the solution of a Riesz equilibrium problem and integral identities for special functions, ,
    Preprints | 2019
    Hamann J; Gia QTL; Sloan IH; Wang YG; Womersley RS, 2019, A New Probe of Gaussianity and Isotropy applied to the CMB Maps,
    Preprints | 2019
    Wang YG; Womersley RS; Wu H-T; Yu W-H, 2019, Numerical computation of triangular complex spherical designs with small mesh ratio, ,
    Preprints | 2018
    Gia QTL; Sloan IH; Womersley RS; Wang YG, 2018, Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere,
    Preprints | 2017
    Brauchart JS; Dragnev PD; Saff EB; Womersley RS, 2017, Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case, ,
    Preprints | 2015
    Brauchart JS; Reznikov AB; Saff EB; Sloan IH; Wang YG; Womersley RS, 2015, Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation,
    Preprints | 2015
    Wang YG; Gia QTL; Sloan IH; Womersley RS, 2015, Fully discrete needlet approximation on the sphere,
    Preprints | 2015
    Wang YG; Sloan IH; Womersley RS, 2015, Riemann localisation on the sphere,
    Preprints | 2014
    Brauchart JS; Dick J; Saff EB; Sloan IH; Wang YG; Womersley RS, 2014, Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces,
    Preprints | 2012
    Chernih A; Sloan IH; Womersley RS, 2012, Wendland functions with increasing smoothness converge to a Gaussian,
    Conference Papers | 2002
    Sloan IH; Womersley RS, 2002, 'The uniform error of hyperinterpolation on the sphere', in 3rd International conference on multivariate approximation theory, Witten-Bommerholz, Germany, presented at 5th International Conference on Multivariate Approximation, Witten-Bommerholz, Germany, 22 September 2002 - 27 September 2002
    Conference Papers | 1999
    Sloan IH; Womersley RS, 1999, 'The search for good polynomial interpolation points on the sphere', in Griffiths DF; Watson GA (ed.), 18th Dundee Biennial Conference on Numerical Analysis, University of Dundee, pp. 211 - 229, presented at 18th Dundee Biennial Conference on Numerical Analysis, University of Dundee, 29 June 1999 - 02 July 1999
    Conference Papers | 1995
    Womersley RS; Lau YK, 1995, 'Portfolio optimisation problems', in Computational Techniques and Applications: Proceedings, Computational Techniques and Applications: CTAC 1995, Singapore, presented at Computational Techniques and Applications: CTAC 1995, Singapore, 11 July 1995 - 14 July 1995
    Conference Papers | 1994
    Chen X; Womersley RS, 1994, 'A parallel inexact Newton method for stochastic programs with recourse', in Annals of Operations Research, Kluwer Academic Publ, Dordrecht, Netherlands, pp. 113 - 141, presented at IFIP Workshop, Lillehammer, Norway,

My research is in the development and application of computational methods for optimization problems, computational mathematics in general, but especially applied to problems of approximation and numerical integration on the sphere, high performance computing and problems in computational finance, such as calibration of financial models to market data.