Jacek Gondzio

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 Martínez)
  
• Numerical Linear Algebra for PDEs and Large Scale Optimization, February 2020
  (Luca Bergamaschi, Angeles Martínez, 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

• EUROPT 2019 Fellow

Editorships

• Member, Editorial Board: Computational Management Science (2002-2009) (flyer)
• Member, Editorial Board: Computational Optimization and Applications (2001-present)
• Member, Editorial Board: European Journal of Operational Research (2015-2023)
• Member, Editorial Board: Mathematical Programming Computation (2008-present)
• Member, Editorial Board: Optimization Methods and Software (2013-present)

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 (2022-2023: MScR) worked on interior point methods for combinatorial optimization;
  
• Artyom Gevorgyan (2024-present) works on fast iterative methods for large linear systems.
  

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).

New survey on IPMs

Interior Point Methods in the Year 2025 (February 2025, published in EURO J on Comp Optimization).

Software development:

  Linear, Quadratic & Convex Nonlinear Optimization with IPMs:
HOPDM (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:
PDCGM (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:
OOPS (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.
53 students attended the Operational Research MSc programme in 2024/2025.
We have started enrolling for the 2025/2026 OR MSc.
For information see Edinburgh OR MSc.

Teaching in 2024/2025:
  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