Select Publications

Books

Qi L; Ruszczynski A; Womersley RS, (eds.), 1997, Computational nonsmooth optimization, Original, Mathematical Programming Society, North Holland

Book Chapters

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, http://dx.doi.org/10.1007/978-3-319-72456-0_10

Hesse K; Sloan IH; Womersley RS, 2015, 'Numerical integration on the sphere', in Handbook of Geomathematics: Second Edition, pp. 2671 - 2710, http://dx.doi.org/10.1007/978-3-642-54551-1_40

Hesse K; Sloan IH; Womersley RS, 2010, 'Numerical Integration on the Sphere', in Freeden W; Nashed MZ; Sonar T (ed.), Handbook of Geomathematics, edn. 1st, Springer, Berlin, pp. 1187 - 1220

Journal articles

Le Gia QT; 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, http://dx.doi.org/10.1016/j.acha.2019.01.005

Womersley RS, 2018, 'Efficient spherical designs with good geometric properties', Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 1243 - 1285, http://dx.doi.org/10.1007/978-3-319-72456-0_57

Chen X; Womersley RS, 2018, 'Spherical designs and nonconvex minimization for recovery of sparse signals on the sphere', SIAM Journal on Imaging Sciences, vol. 11, pp. 1390 - 1415, http://dx.doi.org/10.1137/17M1147378

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, vol. 27, pp. 62 - 81, http://dx.doi.org/10.1080/10586458.2016.1226209

Hesse K; Sloan IH; Womersley RS, 2017, 'Radial basis function approximation of noisy scattered data on the sphere', Numerische Mathematik, vol. 137, pp. 579 - 605, http://dx.doi.org/10.1007/s00211-017-0886-6

Le Gia QT; Sloan IH; Wang YG; Womersley RS, 2017, 'Needlet approximation for isotropic random fields on the sphere', Journal of Approximation Theory, vol. 216, pp. 86 - 116, http://dx.doi.org/10.1016/j.jat.2017.01.001

Wang YG; Le Gia QT; Sloan IH; Womersley RS, 2017, 'Fully discrete needlet approximation on the sphere', Applied and Computational Harmonic Analysis, vol. 43, pp. 292 - 316, http://dx.doi.org/10.1016/j.acha.2016.01.003

Wang YG; Sloan IH; Womersley RS, 2016, 'Riemann Localisation on the Sphere', Journal of Fourier Analysis and Applications, pp. 1 - 43, http://dx.doi.org/10.1007/s00041-016-9496-4

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', Journal of Mathematical Analysis and Applications, http://dx.doi.org/10.1016/j.jmaa.2015.05.079

Brauchart JS; Saff EB; Sloan IH; Womersley RS, 2014, 'QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere', Mathematics of Computation, vol. 83, pp. 2821 - 2851, http://dx.doi.org/10.1090/S0025-5718-2014-02839-1

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, vol. 52, pp. 2205 - 2206, http://dx.doi.org/10.1137/140962504

Chernih A; Sloan IH; Womersley RS, 2014, 'Wendland functions with increasing smoothness converge to a Gaussian', Advances in Computational Mathematics, vol. 40, pp. 185 - 200, http://dx.doi.org/10.1007/s10444-013-9304-5

Hesse K; Womersley RS, 2012, 'Numerical integration with polynomial exactness over a spherical cap', Advances in Computational Mathematics, vol. 36, pp. 451 - 483, http://dx.doi.org/10.1007/s10444-011-9187-2

Sloan IH; Womersley RS, 2012, 'Filtered hyperinterpolation: A constructive polynomial approximation on the sphere', GEM - International Journal on Geomathematics, vol. 3, pp. 95 - 117, http://dx.doi.org/10.1007/s13137-011-0029-7

An C; Chen X; Sloan IH; Womersley RS, 2012, 'Regularized least squares approximations on the sphere using spherical designs', SIAM Journal on Numerical Analysis, vol. 50, pp. 1513 - 1534, http://dx.doi.org/10.1137/110838601

Chen X; Womersley RS; Ye JJ, 2011, 'Minimizing the condition number of a Gram matrix', SIAM Journal on Optimization, vol. 21, pp. 127 - 148, http://dx.doi.org/10.1137/100786022

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, vol. 48, pp. 2135 - 2157, http://dx.doi.org/10.1137/100795140

Sloan IH; Womersley RS, 2009, 'A variational characterisation of spherical designs', Journal of Approximation Theory, vol. 159, pp. 308 - 318, http://dx.doi.org/10.1016/j.jat.2009.02.014

Leopardi PC; Womersley RS, 2008, 'Porting a sphere optimization program from LAPACK to ScaLAPACK', ANZIAM Journal, vol. 50

Polak E; Womersley RS; Yin HX, 2008, 'An algorithm based on active sets and smoothing for discretized semi-infinite minimax problems', Journal of Optimization Theory and Applications, vol. 138, pp. 311 - 328, http://dx.doi.org/10.1007/s10957-008-9355-9

Kuo FY; Dunsmuir WT M; Sloan IH; Wand MP; Womersley RS, 2008, 'Quasi-Monte Carlo for highly structured generalised response models', Methodology and Computing in Applied Probability, vol. 10, pp. 239 - 275, http://dx.doi.org/10.1007/s11009-007-9045-3

Evans JR; Womersley RS; Wong D; Woodbury G, 2008, 'Operational Risk in Banks', JASSA - Journal of the Securities Institute of Australia, vol. 2, pp. 9 - 16

Jeyakumar V; Ormerod J; Womersley RS, 2006, 'Knowledge-based semidefinite linear programming classifiers', Optimization Methods and Software, vol. 21, pp. 693 - 706, http://dx.doi.org/10.1080/10556780500137066

Chen X; Womersley RS, 2006, 'Existence of solutions to systems of underdetermined equations and spherical designs', SIAM Journal on Numerical Analysis, vol. 44, pp. 2326 - 2341, http://dx.doi.org/10.1137/050626636

Sloan IH; Womersley RS, 2004, 'Extremal systems of points and numerical integration on the sphere', Advances in Computational Mathematics, vol. 21, pp. 107 - 125

Polak E; Royset JO; Womersley RS, 2003, 'Algorithms with adaptive smoothing for finite minimax problems', Journal of Optimization Theory and Applications, vol. 119, pp. 459 - 484, http://dx.doi.org/10.1023/B:JOTA.0000006685.60019.3e

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, vol. 149, pp. 227 - 237, http://dx.doi.org/10.1016/S0377-0427(02)00532-0

Sun D; Womersley RS; Qi H, 2002, 'A feasible semismooth asymptotically Newton method for mixed complementarity problems', Mathematical Programming, Series B, vol. 94, pp. 167 - 187, http://dx.doi.org/10.1007/s10107-002-0305-2

Lau KK; Womersley RS, 2001, 'Multistage quadratic stochastic programming', Journal of Computational and Applied Mathematics, vol. 129, pp. 105 - 138, http://dx.doi.org/10.1016/S0377-0427(00)00545-8

Womersley RS; Sloan IH, 2001, 'How good can polynomial interpolation on the sphere be?', Advances in Computational Mathematics, vol. 14, pp. 195 - 226, http://dx.doi.org/10.1023/A:1016630227163

Sloan IH; Womersley RS, 2000, 'Constructive Polynomial Approximation on the Sphere', Journal of Approximation Theory, vol. 103, pp. 91 - 118, http://dx.doi.org/10.1006/jath.1999.3426

Chen X; Womersley RS, 2000, 'Random test problems and parallel methods for quadratic programs and quadratic stochastic programs', Optimization Methods and Software, vol. 13, pp. 275 - 306, http://dx.doi.org/10.1080/10556780008805789

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

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, vol. 9, pp. 388 - 413, http://dx.doi.org/10.1137/S1052623496314173

Khoury F; Standish RK; Womersley RS, 1998, 'Parallel triangular system solvers', New South Wales Centre for Parallel Computine, pp. 21 - 22

Chen X; Womersley RS, 1998, 'Stochastic programming', New South Wales Centre for Parallel Computine, pp. 10 - 10

Tin-Loi F; Qi L; Wei Z; Womersley RS, 1996, 'Stochastic ultimate load analysis: Models and solution methods', Numerical Functional Analysis and Optimization, vol. 17, pp. 1029 - 1043, http://dx.doi.org/10.1080/01630569608816740

Qi L; Womersley RS, 1996, 'On Extreme Singular Values of Matrix Valued Functions', Journal of Convex Analysis, vol. 3, pp. 153 - 166

Qi L; Womersley RS, 1995, 'An SQP algorithm for extended linear-quadratic problems in stochastic programming', Annals of Operations Research, vol. 56, pp. 251 - 285, http://dx.doi.org/10.1007/BF02031711

Chen X; Qi L; Womersley RS, 1995, 'Newton's method for quadratic stochastic programs with recourse', Journal of Computational and Applied Mathematics, vol. 60, pp. 29 - 46, http://dx.doi.org/10.1016/0377-0427(94)00082-C

Overton ML; Womersley RS, 1995, 'Second derivatives for optimizing eigenvalues of symmetric matrices', SIAM Journal on Matrix Analysis and Applications, vol. 16, pp. 697 - 718

Overton ML; Womersley RS, 1993, 'Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices', Mathematical Programming, Series B, vol. 62, pp. 321 - 357

Osborne MR; Womersley RS, 1990, 'Strong uniqueness in sequential linear programming', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol. 31, pp. 379 - 384, http://dx.doi.org/10.1017/s0334270000006731

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, vol. 9, pp. 473 - 498, http://dx.doi.org/10.1137/0609040

Womersley RS, 1986, 'Censored Discrete Linear $l_1 $ Approximation', SIAM Journal on Scientific and Statistical Computing, vol. 7, pp. 105 - 122, http://dx.doi.org/10.1137/0907008

Osborne MR; Pruess SA; Womersley RS, 1986, 'Concise representation of generalised gradients', The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, vol. 28, pp. 57 - 74, http://dx.doi.org/10.1017/s0334270000005191


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