Dr Sándor Zoltán Németh MSc PhD

Dr Sándor Zoltán Németh

School of Mathematics
Associate Professor

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Sándor Zoltán Németh is an Associate Professor in Optimisation, in Theoretical and Computational Optimisation Group.

Sándor's recent research areas are Optimisation on Manifolds, Convex Optimisation and Equilibrium Systems. Sándor is especially interested in the connections between these areas. Sándor's other main topics of interest are Ordered Vector Spaces, Cones and Projection Operators.

Sándor has published 1 book, 4 book chapters and over 60 research papers in scientific journals in the fields of Optimisation, Nonlinear Analysis, Multicriteria Decision Problems, Differential Geometry, Linear Algebra, Artificial Intelligence, Fluid Mechanics, Elementary Geometry.

Personal webpage


  • PhD in Mathematics Eötvös Loránd University, Budapest, Hungary 1999
  • MSc (a degree equivalent to MSc) in Mathematics, Babeş-Bolyai University 1993


Sándor Zoltán Németh qualified with a (degree equivalent to) MSc in Mathematics from the Babes-Bolyai University, Cluj-Napoca, Romania as chief of promotion. He obtained a PhD in Mathematics at the Eötvös Loránd University, Budapest, Hungary.

Sándor has obtained the following Scholarships and Awards:

  • 1989: 3rd prize at the university's Olympiad
  • 1989: 2nd prize at the university's Scientific Student Conference
  • 1992/93: Tempus scholarship, The University of Edinburgh, Scotland, U.K.
  • 1995-1998: Scholarship of the Hungarian Ministry of Education
  • 1998-2001: Bolyai János fellowship of the Hungarian Academy of Sciences
  • 2000: Farkas Gyula prize for Applied Mathematics of the Bolyai János Mathematical Society

Previous positions:

  • 2002-2003: Honorary Research Fellow, School of Computer Science, University of Birmingham
  • 1999-2005: Senior Researcher, Laboratory of Operations Research and Decision Systems, Computer and Automation Institute, Hungarian Academy of Sciences
  • 2001 autumn term: External Lecturer, School of Mechanical Engineering, University of Birmingham
  • 1993-1995: Teaching Assistant, Chair of Geometry, Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania

Sándor was a Stream Organizer for nine EURO conferences, the latest two of them the Mathematical Programming Stream of the EURO XXX Conference, Dublin, Ireland, June 23-26, 2019 and the 'Nonlinear Programming: Theory' Stream of the EURO XXIX Conference, Valencia, Spain, July 8-11, 2018.

Four PhD students and two Mphil students have obtained their degrees under Sándor's supervision and he is currently supervising two PhD students.

Sándor is a language enthusiast. He has a native/bilingual proficiency in Hungarian and Romanian, full professional proficiency in English, professional proficiency in Portuguese, limited working proficiency in Spanish and Italian, elementary proficiency in French and Catalan.


Semester 1

LH/LM Non-linear Programming and Heuristic Optimisation

Semester 2

LH/LM Game Theory and Multicriteria Decision Making

Postgraduate supervision

Sándor is supervising postgraduate students in Optimisation on Manifolds, Convex Optimisation, Equilibrium Systems, Ordered Vector Spaces and Multicriteria Decision Making.


Research themes

  • Optimisation on Manifolds
  • Convex Optimisation
  • Equilibrium Systems
  • Ordered Vector Spaces
  • Multicriteria Decision Problems
  • Artificial Intelligence

Research activity

In the past Sándor has initiated the concepts of monotone vector fields, scalar derivatives, lattice-like operations and isotone retractions and together with his co-authors has connected them to optimisation on manifolds, convex optimisation, projection operators, equilibrium problems and isotonic regression. Sándor has also contributed to the mathematics part of important papers about fitness sharing and limitation of code growths in genetic programming. His most recent interests are in the following topics:

Optimisation on Riemannian Manifolds and Applications

Sándor is interested in the geodesic convexity and the optimisation of quadratic functions on the sphere. This topic is motivated by a wide range of applications such as solid mechanics, signal processing, computational anatomy and quantum mechanics. Besides the practical interest, many optimisation problems are naturally posed on the sphere, which has an underlying algebraic structure that can be greatly exploited to find efficient solutions.

Sándor is interested in convexity/optimisation on the Hyperbolic space. The hyperbolic space is of central interest in relativity, but recently became important in specific problems of machine learning, financial mathematics and geology too. He is working on the convexity of quadratic functions, duality, existence of solutions and their approximation.

Sándor is interested in the study of the convergence of the first order gradient based algorithms for manifolds of unbounded sectional curvature, which is an important open question.

Sándor is initiating the study of the Stiefel manifold of orthonormal 2-frames, and its connections with complementarity problems and duality in optimisation.

New Cones, Ordered Vector Spaces, Complementarity Problems, Variational Inequalities and Equilibrium, and Applications

Sándor is interested in extensions of the second order cone. He has introduced two new cones the extended second order cone and the monotone extended second order cone. Both of them can be used to model specific portfolio optimisation problems. With his coauthors he studied the structure of these cones and designed efficient methods to project onto them.

The cones mentioned in the previous item have good ordering properties which can be used to solve general complementarity problems and variational inequalities. Solving such problems is important because many equilibrium problems in economics, finance, physics, mechanics and traffic can be described as complementarity problems or variational inequalities. The Karush-Kuhn-Tucker conditions for the portfolio optimisation problems related to the aforementioned cones are complementarity problems on them. The study/solution of these portfolio optimisation problems can be done via the corresponding complementarity problems.

Other activities

Sándor is currently the Data Tsar of Mathematics. His previous admin roles include: Director of Graduate School, Director of MSc Financial Engineering, and Director of 3rd Year BSc.

Sándor is an Associate Editor of the Journal of Optimization and Applications, and the International Journal of Computer Mathematics.


Recent publications


Ferreira, O, Gao, Y, Nemeth, S & Rigó, PR 2024, 'Gradient projection method on the sphere, complementarity problems and copositivity', Journal of Global Optimization. https://doi.org/10.1007/s10898-024-01390-4

Ferreira, O, Nemeth, S & Zhu, J 2023, 'Convexity of non-homogeneous quadratic functions on the hyperbolic space', Journal of Optimization Theory and Applications, vol. 199, no. 3, pp. 1085-1105. https://doi.org/10.1007/s10957-023-02332-y

Ferreira, O, Nemeth, S & Zhu, J 2022, 'Convexity of sets and quadratic functions on the hyperbolic space', Journal of Optimization Theory and Applications, vol. 2022. https://doi.org/10.1007/s10957-022-02073-4

Nemeth, AB & Nemeth, S 2022, 'Izoton vetítések és alkalmazásaik', Alkalmazott Matematikai Lapok, vol. 39, no. 2, pp. 1-11.

Ferreira, O, Gao, Y & Nemeth, S 2022, 'Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression', Optimization, vol. 2022, pp. 1-15. https://doi.org/10.1080/02331934.2022.2103415

Gao, Y, Nemeth, S & Sznajder, R 2022, 'The monotone extended second-order cone and mixed complementarity problems', Journal of Optimization Theory and Applications, vol. 193, no. 1-3, pp. 381-407. https://doi.org/10.1007/s10957-021-01962-4

Ferreira, O, Nemeth, S & Xiao, L 2020, 'On the Spherical Quasi-Convexity of Quadratic Functions on Spherically Subdual  Convex Sets', Journal of Optimization Theory and Applications, vol. 187, no. 1, pp. 1-21. https://doi.org/10.1007/s10957-020-01741-7

Ferreira, O & Nemeth, S 2019, 'On the spherical convexity of quadratic function', Journal of Global Optimization, vol. 73, pp. 537–545. https://doi.org/10.1007/s10898-018-0710-6

Ferreira, O, Nemeth, S & Xiao, L 2019, 'On the spherical quasi-convexity of quadratic functions', Linear Algebra and its Applications, vol. 562, pp. 205-222. https://doi.org/10.1016/j.laa.2018.10.011

Nemeth, S, Xie, J & Zhang, G 2019, 'Positive operators on extended second order cones', Acta Mathematica Hungarica, vol. 160, pp. 390-404. https://doi.org/10.1007/s10474-019-01011-7

Nemeth, S & Gowda, MS 2019, 'The cone of Z-transformations on the Lorentz cone', Electronic Journal of Linear Algebra, vol. 35, no. 1, 25, pp. 387-393. https://doi.org/10.13001/1081-3810.4083

Ferreira, O & Nemeth, S 2018, 'How to project onto extended second order cones', Journal of Global Optimization, vol. 70, no. 4. https://doi.org/10.1007/s10898-017-0587-9

Nemeth, S & Xiao, L 2018, 'Linear complementarity problems on extended second order cones', Journal of Optimization Theory and Applications, vol. 176, no. 2, pp. 269-288. https://doi.org/10.1007/s10957-018-1220-x

Bello Cruz, JY, Ferreira, O, Nemeth, S & Prudente, LDF 2017, 'A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone', Linear Algebra and its Applications, vol. 513, pp. 160-181. https://doi.org/10.1016/j.laa.2016.10.007

Nemeth, S, Barrios, J, Bello Cruz, JY & Ferreira, O 2016, 'A semi-smooth Newton method for a special piecewise linear system with application to positively constrained convex quadratic programming', Journal of Computational and Applied Mathematics, vol. 301, pp. 91–100. https://doi.org/10.1016/j.cam.2016.01.040

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