Vera Roshchina

Mathematician at UNSW Sydney

I am an applied mathematician working on convex and nonsmooth problems that mostly come from optimisation.

Before joining the School of Mathematics and Statistics of UNSW Sydney in 2018 I was an ARC DECRA Research Fellow at RMIT University and held postdoctoral positions at the The University of Melbourne, Federation University Australia and University of Évora. I got my undergraduate degree from from St-Petersburg State University and my PhD is from the City University of Hong-Kong.

Publications

  1. Reinier Díaz Millán, Vera Roshchina, The intrinsic core and minimal faces of convex sets in general vector spaces (2021), arXiv:2107.07730
  2. Bruno Lourenço, Vera Roshchina, James Saunderson, Hyperbolicity cones are amenable (2021), arXiv:2102.06359.
  3. Bruno Lourenço, Vera Roshchina, James Saunderson, Amenable cones are particularly nice (2020), arXiv:2011.07745.
  4. Javier Peña, Vera Roshchina, A data-independent distance to infeasibility for linear conic systems, SIAM J. Optim. 30, 1049–1066 (2020), arXiv:1805.09494.
  5. Ryan McKewen, Vera Roshchina, Dimension and structure of higher-order Voronoi cells on discrete sites, 11 December 2019, arXiv:1912.05102.
  6. Vera Roshchina, Nadia Sukhorukova and Julien Ugon, Uniqueness of solutions in multivariate Chebyshev approximation problems, 30 August 2019, arXiv:1908.11570.
  7. Alexander Plakhov, Vera Roshchina, Invisibility in billiards is impossible in an infinite number of directions, J Dyn Control Syst 25(4), 671–679 (2019), arXiv:1206.6965v1.
  8. Juan Enrique Martínez-Legaz, Vera Roshchina, Maxim Todorov, On the Structure of Higher Order Voronoi Cells, J. Optim. Theory Appl. 183(1), 24–49 (2019), arXiv:1811.10257.
  9. Hector Ramirez, Vera Roshchina, Refining the partition for multifold conic optimization problems, Optimization 69(11) 2489–2507 (2020), arXiv:1804.00386.
  10. Vera Roshchina and Levent Tunçel, Facially Dual Complete (Nice) cones and lexicographic tangents, SIAM J. Optim. Vol. 29, Issue 3, 2363–2387 (2019), arXiv:1704.06368.
  11. Reinier Díaz Millán, Scott B. Lindstrom, Vera Roshchina, Comparing Averaged Relaxed Cutters and Projection Methods: Theory and Examples, accepted to Special Springer Volume commemorating Jon Borwein, Springer Proceedings in Mathematics & Statistics, 2018, arXiv:1810.02463.
  12. Bui Thi Hoa, Scott Lindstrom, Vera Roshchina, Variational Analysis Down Under Open Problem Session, J. Optim. Theory Appl. 182(1), 430-437 (2019), arXiv:1806.01163.
  13. A. Eberhard, V. Roshchina, T. Sang, Outer limits of subdifferentials for min-max type functions, Optimization 68(7), 1391–1409 (2017), arXiv:1701.02852.
  14. V. Roshchina, The Demyanov-Ryabova conjecture is false, Optim. Lett. 13(1), 227–234 (2019), arXiv:1803.05614.
  15. R. Cominetti, V. Roshchina, A. Williamson, A counterexample to De Pierro’s conjecture on the convergence of under-relaxed cyclic projections, Optimization 68(1), 3–12 (2019), arXiv:1801.03216
  16. V. Roshchina, T. Sang, D. Yost, Compact Convex Sets with Prescribed Facial Dimensions, Wood D., de Gier J., Praeger C., Tao T. (eds) 2016 MATRIX annals, 167–175, MATRIX Book Ser., 1 (2018), arXiv:1610.02737
  17. W. Achtziger, R. Baier, E. Farkhi, V. Roshchina, Exact Penalty and Lagrange Duality via the Directed Subdifferential, Pure and Applied Functional Analysis Volume 2 Number 2, 183–220 (2017).
  18. Baier R., Farkhi, E., Roshchina, V., From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules, J. Optim. Theory Appl. 171, 384–401 (2016). arXiv:1507.00174
  19. Cucker, F., Peña, J., Roshchina, V., Solving second-order conic systems with variable precision. Math. Progr., 150, 217-250 (2015). arXiv:1104.1352v1
  20. Meng, K., Roshchina, V., Yang, X., On Local Coincidence of a Convex Set and its Tangent Cone. J. Optim. Theory Appl. 164, 123-137 (2014).
  21. Peña, J., Roshchina, V., Soheili, N., Some preconditioners for systems of linear inequalities. Optim. Lett., 8, 2145-2152 (2014). arXiv:1306.5287
  22. Plakhov, A., Roshchina, V., Bodies with mirror surface invisible from two points, Nonlinearity 27, 1193 (2014), arXiv:1304.4005.
  23. Roshchina, V., Facially exposed cones are not always nice. SIAM J. Optim. 24, 257–268 (2014). arXiv:1301.1000
  24. Baier, R., Farkhi, E., Roshchina, V., Directed Subdifferentiable Functions and the Directed Subdifferential Without DC Structure, J. Optim. Theory Appl. 160, 391–414 (2014). arXiv:1212.1508
  25. Briquel, I., Cucker, F., Peña, J., Roshchina, V., Fast Computation of Zeros of Polynomial Systems with Bounded Degree under Finite-precision. Math.Comp. 83, 1279–1317 (2014) arXiv:1205.0869
  26. Plakhov A., Roshchina, V., Bodies invisible from one point. arXiv:1112.6167v1
  27. Peña, J., Roshchina, V., A Complementarity Partition Theorem for Multifold Conic Systems. Mathematical Programming 142, 579-589 (2013), arXiv:1108.0760v1
  28. Plakhov, A., Roshchina, V., Fractal bodies invisible in 2 and 3 directions, Discrete and Continuous Dynamical Systems A, 33, 1615-1631 (2012). arXiv:1107.5667v1
  29. Lakshtanov, E., Roshchina, V., Finiteness in the Card Game of War. The American Mathematical Monthly 119, 318-323 (2012). arXiv:1007.1371v1
  30. Baier, R., Farkhi, E., Roshchina, V., The Directed and Rubinov Subdifferentials of Quasidifferentiable Functions. Part I: Definition and Examples. Nonlinear Analysis, Volume 75, pp. 1074-1088.
  31. Baier, R., Farkhi, E., Roshchina, V., The Directed and Rubinov Subdifferentials of Quasidifferentiable Functions. Part II: Calculus. Nonlinear Analysis, Volume 75, pp. 1058-1073.
  32. Plakhov, A., Roshchina, V., Invisibility in billiards. Nonlinearity, Volume 24, pp. 847-854 (2011); arXiv:1009.1104
  33. Mordukhovich, B., Peña, J., Roshchina, V., Applying Metric Regularity To Compute Condition Measure of Smoothing Algorithm for Matrix Games. SIAM J. Optim. Volume 20, Issue 6, pp. 3490-3511 (2010); arXiv:1007.4458
  34. Baier, R., Farkhi, E., Roshchina, V., On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions. Variational Analysis and Generalized Differentiation in Optimization and Control. Optimization and Its Applications, Volume 47, pp. 59-93 (2010).
  35. Roshchina, V., Mordukhovich subdifferential of pointwise minimum of approximate convex functions. Optim. Methods Softw., Volume 25, Issue 1, February 2010, 129-141.
  36. Roshchina, V., Exact calculus of Fréchet subdifferentials for Hadamard directionally differentiable functions. Nonlinear Anal., Volume 69, Issue 4, 15 August 2008, 1112-1124.
  37. Li, D., Qi, L., Roshchina, V., A New Class of Quasi-Newton Updating Formulas. Optim. Methods Softw., Vol. 23 Issue 2, 237-249 (Apr 2008).
  38. Demyanov V.F., Roshchina V., Exhausters, optimality conditions and related problems. J. Global Optim., Vol. 40 No. 1-3, 71-83 (Mar 2008).
  39. Roshchina V.A., Reducing Exhausters. J. Optim. Theory Appl., Vol. 136, No. 2, 261-273 (Feb 2008).
  40. Demyanov V.F., Roshchina V., Exhausters and subdifferentials in Nonsmooth Analysis. Optimization, Vol. 57 No 1, 41-56 (Feb 2008).
  41. Roshchina V.A., On Conditions for the Minimality of Exhausters. J. Convex Anal. Vol. 15, No. 4 (2008).
  42. Demyanov, V.F., Roshchina, V., Generalized Subdifferentials and Exhausters in Nonsmooth Analysis. Translation from Russian in Doklady. Mathematics, Vol. 76, No. 2, 652-655
  43. Roshchina, V., Relationships between upper exhausters and the basic subdifferential in Variational Analysis. J. Math. Anal. Appl., 334 261-272 (2007).
  44. Demyanov, V.F., Roshchina, V., Generalized Subdifferentials and Exhausters. Vladikavkaz Mathematical Journal, Vol. 8, No. 4 (2006) (in Russian)
  45. Demyanov V.F., Roshchina V.A. Optimality conditions in terms of upper and lower exhausters. Optimization, Vol. 55, No. 5-6, 525-540 (Oct-Dec 2006).
  46. Demyanov V.F., Roshchina V.A. Constrained Optimality Conditions in Terms of Proper and Adjoint Exhausters. Appl. Comput. Math.,Vol. 4, No. 2, 144-124 (2005).

Past Research Activities

2021

Workshop on Optimisation, Metric Bounds, Approximation and Transversality (WOMBAT2021), 13–17 December 2021

https://wombat.mocao.org/

Workshop on the Intersections of Computation and Optimisations (WICO), 22–25 November 2021

https://maths.anu.edu.au/news-events/events/workshop-intersections-computation-and-optimisations

SIAM Conference on Optimization (OP21), 20-23 July 2021

https://www.siam.org/conferences/cm/conference/op21

Well-posedness of optimization problems and related topics, 28 June–2 July 2021

http://www.math.bas.bg/~bio/WP21/

2020

WOMBAT 2020, Geelong campus of Deakin University, 2–4 December 2020

www.wombat.mocao.org

Computational Techniques and Applications Conference (CTAC2020), 30 August–2 September 2020

https://www.ctac2020.unsw.edu.au/

2019

WoMBaT 2019, 8-10 December 2019

www.wombat.mocao.org

“63nd” Annual Meeting of the Australian Maths Society, 3-6 December 2019

https://www.austms.org.au/tiki-calendar.php?calitemId=900

Integrable Systems 2019, 28–29 November 2019

http://wp.maths.usyd.edu.au/igs/workshops/integrable-systems-2019/

Workshop on Geometry and Optimisation, 5–6 November 2019

https://www.maths.unsw.edu.au/events/2019-11/workshop-geometry-and-optimisation

See here for archived information.

14th International Seminar on Optimization and Related Areas (ISORA), 7–11 October 2019

http://isora2019.imca.edu.pe/

Workshop Chile-Australia on Optimization (WACHO 2019), 2 October 2019

http://www.cmm.uchile.cl

Complexity of numerical computation: a workshop in honour of Felipe Cucker, 19–23 August 2019

http://felipefest.xyz/

Workshop on Mathematical Billiards, 24–27 June 2019

https://www.maths.usyd.edu.au/u/billiards/

BIRS workshop: Geometry of Real Polynomials, Convexity and Optimization, 26–31 May 2019

https://www.birs.ca/events/2019/5-day-workshops/19w5180

2018

WoMBaT 2018, 29 November–1 December 2018

http://www.wombat.mocao.org/

CTAC 2018, 27–30 November 2018

https://carma.newcastle.edu.au/meetings/ctac2018/

AVOCADO, 25–26 August 2018

Conference poster

Workshop on Fixed Points and Applications, 21 May 2018

This one-day workshop was held at RMIT, and was focussed around the research interests of Professor Hong-Kun Xu who was visiting me at that time. See here for more information about this workshop, also https://sites.rmit.edu.au/rmitopt/fpaa/.

MATRIX program on Approximation, Optimisation and Algebraic Geometry, February 2018

https://www.matrix-inst.org.au/events/algebraic-geometry-approximation-and-optimisation/

Variational Analysis Down Under (VADU2018) in honour of Asen Dontchev, 19–21 February 2018

https://sites.rmit.edu.au/asen/

2017

WoMBaT 2017, 29 November–2 December 2017

http://www.wombat.mocao.org/

SPOM in Western Australia, 8–10 December 2017

http://scieng.curtin.edu.au/science/mathematics-and-statistics/joc-2017/spom-in-wa-2017/

2016

Workshop on polytopes, 17 November 2016

An informal gathering of those interested in the geometry of polytopes. See here for more information about this workshop.

WoMBaT 2016, 24–25 November

http://www.wombat.mocao.org/wombat-2016/wombat-2016-overview/

MATRIX Program on Approximation and Optimisation

The program was held on 11-16 July in Creswick, Victoria.

MODU2016 workshop, 18-22 July 2016

The workshop was designed to bring together researchers working in various areas of modern mathematical optimisation, to prompt an exchange of ideas between Australian and overseas researchers. The workshop was focussed on the modern aspects of optimisation that involve deep interplay between computational problems and pure mathematical questions.

Please visit here for more info.

Current Teaching

Honours level courses

Optimisation for Deep Learning (2020-2021)

This course endorsed by MoCaO special interest group of AustMS is taught via the AMSI ACE network in collaboration with Dr Nadia Sukhorukova (Swinburne University of Technology) and Dr Julien Ugon (Deakin University).

The goal is to provide theoretical foundations of the optimisation theory, and apply it to formulate and solve optimisation problems appearing in deep learning models using a range of optimisation techniques. More information is available on the course page http://www.mocao.org/odl/.

Undergraduate courses

Several Variable Calculus MATH2011 (2019-2021)

MATH2011 is a  second year calculus course that covers the fundamentals of vector calculus including Lagrange multipliers, Green, Stokes’ and divergence theorems and Fourier series.

Higher Mathematics MATH1231 (Algebra, 2019-2021)

MATH1231 is a first year algebra/calculus course.