Research Interests
- Large scale optimization
- interior point methods for LP, QP and NLP
- cutting plane methods for convex optimization
- simplex-type methods for LP
- Sparse matrix methods in optimization
- linear algebra techniques of optimization
- structure exploiting techniques in dynamic, stochastic or network optimization
- Parallel computing techniques in optimization
- parallel methods of linear algebra
- parallel decomposition methods
Workshops Organised in Edinburgh
-
Linear Algebra and Optimization, October 2013
(Jacek Gondzio and Rachael Tappenden)
-
Convex Optimization and Beyond, June 2014
(Jacek Gondzio and Julian Hall)
Keynote speaker: Stephen Boyd, Stanford University, USA
-
Computational Optimization in Action 2016, June 2016
(Jacek Gondzio and Julian Hall)
Keynote speaker: Prof Michael C. Ferris, University of Wisconsin, USA
-
Advances in Preconditioners, March 2017
(Jacek Gondzio and Lukas Schork)
-
Preconditioning Iterative Methods in Optimization, November 2017
(Alemseged Weldeyesus and Jacek Gondzio)
-
Computational Optimization in Action, June 2018
(Jacek Gondzio and Julian Hall)
Keynote speaker: Prof Immanuel Bomze, University of Vienna, Austria
-
Recent Advances in Models and Methods for Optimization of Truss Structures, June 2018
(Alemseged Weldeyesus and Jacek Gondzio)
-
Semidefinite Programming: Theory and Applications, October 2018
(Alemseged Weldeyesus and Jacek Gondzio)
Keynote speaker: Prof Christoph Helmberg, Chemnitz University of Technology, Germany
-
Advances in Linear Algebra and Huge-Scale Optimization, July 2019
(John Pearson, Jacek Gondzio, Luca Bergamaschi and Angeles MartÃnez)
-
Numerical Linear Algebra for PDEs and Large Scale Optimization, February 2020
(Luca Bergamaschi, Angeles MartÃnez, Jacek Gondzio and John Pearson)
-
Modern Techniques of Very Large Scale Optimization, May 2022 (initially planned in June 2020)
(Jacek Gondzio, Stefano Cipolla and Filippo Zanetti)
Ongoing Research Projects
-
Computational design optimization of large-scale building structures:
methods, benchmarking and applications
(2016-2019) EP/N019652/1 (EPSRC grant).
-
IP-MATCH: Integer programming for large and complex matching problems
(2017-2020) EP/P029825/1 (EPSRC grant)
(with Sergio Garcia Quiles and Joerg Kalcsics).
-
Fast interior point method for linear programming problems
(2017-2018) Google Research Award, Google, Paris, France.
-
Risk concentration measurement
(2016-2020) (EPSRC Impact Acceleration Account and Standard Life Investments)
(with Sergio Garcia Quiles, Joerg Kalcsics and Sotirios Sabanis).
-
Randomly sampled cyclic alternating direction method of multipliers
(2018-2021) Oracle Labs Research Award, Oracle Labs, Redwood Shores, CA 94065, USA.
-
Matrix-free preconditioners for large-scale convex
constrained optimization problems
(2019-2020) University of Padova, Italy
(with Luca Bergammaschi, Angeles Martinez and John Pearson).
-
Fast (1+x)-order methods for linear programming problems
(2020-2021) Google Research Award, Google, Paris, France.
Awards
Editorships
PhD/MPhil Students:
- Marco Colombo
(2003-2007: PhD) worked on theory and implementation of interior point methods;
- Cathy Buchanan
(2003-2007: MPhil) worked on optimal control problems;
- Ghussoun Al-Jeiroudi
(2004-2009: PhD) worked on iterative methods for KKT systems;
- Kristian Woodsend
(2005-2009: PhD) worked on optimization methods applied in machine learning;
- Xi Yang
(2005-2010: PhD) worked on optimization problems arising in risk modelling;
- Qun Zhang
(2009-2010: MSc by Research) worked on quantitative analysis of structured financial products;
- Pablo González
(2009-2013: PhD) worked on interior point methods for combinatorial optimization;
- Pedro Munari Jr
(2009-2013: PhD) worked on interior point methods for combinatorial optimization;
- Kimon Fountoulakis
(2011-2015: PhD) worked on applications of matrix-free interior point methods;
- Robert Gower
(2012-2016: PhD) worked on nonlinear optimization;
- Lukas Schork
(2015-2018: PhD) worked on inexact interior point methods;
- Spyros Pougkakiotis
(2017-2022: PhD) worked on preconditioners for interior point methods;
- Kresimir Mihic
(2018-2021: PhD) worked on alternating direction method of multipliers for large-scale optimization;
- Filippo Zanetti
(2019-2023: PhD) worked on fast methods for large-scale optimization;
- Siemen Nooren
(2022-) works on interior point methods for combinatorial optimization.
Very Large-Scale Constrained NonLinear Optimization
Together with Andreas Grothey we solved (May 2005) a large financial
planning problem:
a quadratic program with 353 million constraints
and 1010 million variables.
Matrix-Free Interior Point Method
Read about the
Matrix-Free IPM (Oct 2009, published in COAP).
Survey on IPMs:
IPMs 25 Years Later (Feb 2011, published in EJOR).
Theoretical background:
Inexact Search Directions in IPMs (July 2012, published in SIOPT).
Application:
Quantum Information (April 2012, published in J of CAM).
2nd Order Methods for Big Data (Convex, Unconstrained) Optimization
Read about the
2nd order method for solving L1-regularization problems
(April 2014, published in Math Prog A).
Read about solving the
Big Data optimization problem of size one trillion (2^40)
(March 2015, published in COAP).
Software development:
Linear, Quadratic & Convex Nonlinear Optimization with IPMs:
(Higher Order Primal-Dual Method)
is an efficient implementation of the multiple centrality correctors
variant of the primal-dual method for large scale linear and convex
quadratic optimization.
An option to work matrix-free has recently been added to it.
The earlier version of HOPDM is available for research use.
Column Generation/Cutting Planes with IPMs:
(Primal-Dual Column Generation Method)
is an interior point based environment for decomposition and
nondifferentiable optimization. The code is available for research use.
Parallel Large-Scale Optimization with IPMs:
(Object-Oriented Parallel structure exploiting
interior point Solver) is a new generation of software for optimization
of unequalled computing power.
24 students attended the Operational Research MSc programme in 2002/2003.
27 students attended the Operational Research MSc programme in 2003/2004.
23 students attended the Operational Research MSc programme in 2004/2005.
31 students attended the Operational Research MSc programme in 2005/2006.
41 students attended the Operational Research MSc programme in 2006/2007.
46 students attended the Operational Research MSc programme in 2007/2008.
52 students attended the Operational Research MSc programme in 2008/2009.
41 students attended the Operational Research MSc programme in 2009/2010.
58 students attended the Operational Research MSc programme in 2010/2011.
55 students attended the Operational Research MSc programme in 2011/2012.
65 students attended the Operational Research MSc programme in 2012/2013.
45 students attended the Operational Research MSc programme in 2013/2014.
47 students attended the Operational Research MSc programme in 2014/2015.
61 students attended the Operational Research MSc programme in 2015/2016.
44 students attended the Operational Research MSc programme in 2016/2017.
47 students attended the Operational Research MSc programme in 2017/2018.
78 students attended the Operational Research MSc programme in 2018/2019.
72 students attended the Operational Research MSc programme in 2019/2020.
90 students attended the Operational Research MSc programme in 2020/2021.
64 students attended the Operational Research MSc programme in 2021/2022.
60 students attended the Operational Research MSc programme in 2022/2023.
35 students attended the Operational Research MSc programme in 2023/2024.
We have started enrolling for the 2024/2025 OR MSc.
For information see
Edinburgh OR MSc.
Teaching in 2023/2024:
MATH11147: Large Scale Optimization for Data Science (Semester 2, Y4/5 Maths and several MSc's)
Address and phone numbers
- J. Gondzio
School of Mathematics
The University of Edinburgh
James Clerk Maxwell Building
Peter Guthrie Tait Road
King's Buildings, EH9 3FD Edinburgh, UK.
- Phone: +44 131 650 8574
- E-mail: J.Gondzio@ed.ac.uk