Edinburgh Research Group in Optimization

C. Cartis, N.I.M. Gould and Ph.L. Toint On the evaluation complexity of cubic regularization methods for potentially rank-deficient nonlinear least-squares problems and its relevance to constrained nonlinear optimization Technical Report ERGO 12-001, School of Mathematics.

C. Cartis, N.I.M. Gould and Ph.L. Toint How much patience do you have? A worst-case perspective on smooth nonconvex optimization Technical Report ERGO 12-002, School of Mathematics.

E. Smith and J.A.J. Hall A high performance primal revised simplex solver for row-linked block angular linear programming problems Technical Report ERGO 12-003, School of Mathematics.

J. Gondzio, J. Gruca, J.A.J. Hall, W. Laskowski and M. Zukowski Solving large-Scale optimization problems related to Bell's theorem Technical Report ERGO 12-004, School of Mathematics.

M. Lubin, J.A.J. Hall, C.G. Petra and M. Anitescu Parallel distributed-memory simplex for large-scale stochastic LP problems Technical Report ERGO 12-005, School of Mathematics.

2011

J. Gondzio, P. González-Brevis, P. Munari New developments in the primal-dual column generation technique Technical Report ERGO 11-001, School of Mathematics.

C. Cartis, N.I.M. Gould and Ph.L. Toint On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming Technical Report ERGO 11-002, School of Mathematics.
Published in SIAM Journal of Optimization.

J. Gondzio Interior Point Methods 25 Years Later Technical Report ERGO 11-003, School of Mathematics.
Published in European Journal of Operational Research.

P.-J. Chung, H. Du, J. Gondzio A probabilistic constraint approach for robust transmit beamforming with imperfect channel information Technical Report ERGO 11-004, School of Mathematics.
Published in IEEE Transactions on Signal Processing.

C. Cartis, N.I.M. Gould and Ph.L. Toint On the complexity of finding first-order critical points in constrained nonlinear programming Technical Report ERGO 11-005, School of Mathematics.

A. Thompson Compressive single-pixel imaging Technical Report ERGO 11-006, School of Mathematics.

J.A.J. Hall and Q. Huangfu A high performance dual revised simplex solver Technical Report ERGO 11-007, School of Mathematics.

E. Smith, J. Gondzio and J.A.J. Hall GPU acceleration of the matrix-free interior point method Technical Report ERGO 11-008, School of Mathematics.
To appear in Lecture Notes in Computer Sciences.

C. Cartis, N.I.M. Gould and Ph.L. Toint Optimal Newton-type methods for nonconvex smooth optimization problems Technical Report ERGO 11-009, School of Mathematics.

S. Bellavia, J. Gondzio and B. Morini New matrix-free preconditioner for sparse least-squares problems Technical Report ERGO 11-010, School of Mathematics.

P. Richtárik and M. Takáč Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function Technical Report ERGO 11-011, School of Mathematics.

P. Richtárik and M. Takáč Efficient serial and parallel coordinate descent methods for huge-scale truss topology design Technical Report ERGO 11-012, School of Mathematics.

C. Cartis, N.I.M. Gould and Ph.L. Toint A note about the complexity of minimizing Nesterov's smooth Chebyshev-Rosenbrock function Technical Report ERGO 11-013, School of Mathematics.

N.-Y. Chiang and A. Grothey Solving security constrained optimal power flow problems by a structure exploiting interior point method Technical Report ERGO 11-014, School of Mathematics.

P.A. Trodden, W.A. Bukhsh, A. Grothey and K.I.M. McKinnon MILP formulation for islanding of power networks Technical Report ERGO 11-015, School of Mathematics.

P.A. Trodden, W.A. Bukhsh, A. Grothey and K.I.M. McKinnon MILP islanding of power networks by bus splitting Technical Report ERGO 11-016, School of Mathematics.
To appear in 2012 IEEE Power Engineering Society General Meeting.

W.A. Bukhsh, A. Grothey, K.I.M. McKinnon and P.A. Trodden Local solutions of optimal power flow Technical Report ERGO 11-017, School of Mathematics.

V. Gunnerud, B.A. Foss, K.I.M. McKinnon and B. Nygreen Oil production optimization solved by piecewise linearization in a branch & price framework Technical Report ERGO 11-018, School of Mathematics.
Published in Computers and Operations Research.

R. Paulavičius, J. Žilinskas and A. Grothey Parallel branch and bound for global optimization with combination of Lipschitz bounds Technical Report ERGO 11-019, School of Mathematics.
Published in Optimization Methods and Software.

A. Grothey Massively parallel asset and liability management Technical Report ERGO 11-020, School of Mathematics.
Published in Lecture Notes in Computer Sciences.

J. Gondzio and P. Zhlobich Multilevel quasiseparable matrices in PDE-constrained optimization Technical Report ERGO 11-021, School of Mathematics.

K.I.M. McKinnon and Y. Yu Solving stochastic ship fleet routing problems with inventory management using branch and price Technical Report ERGO 11-022, School of Mathematics.

2010

E. Fragnière, J. Gondzio, N.S. Tuchschmid and Q. Zhang Non-parametric liquidity adjusted VaR model: a stochastic programming approach Technical Report ERGO 10-001, School of Mathematics.
Published in Journal of Financial Transformation.

P. González-Brevis, J. Gondzio, Y. Fan, H.V. Poor, J. Thompson, I. Krikidis and P.-J. Chung Base station location optimization for minimal energy consumption in wireless networks Technical Report ERGO 10-002, School of Mathematics.

A. Grothey and X. Yang Solving the top-percentile traffic routing problem by approximate dynamic programming Technical Report ERGO 10-003, School of Mathematics.

J. Gondzio Interior point methods in machine learning Technical Report ERGO 10-004, School of Mathematics.
Published in S. Sra, S. Nowozin and S. Wright (eds), Optimization for Machine Learning, MIT Press, 2010.

C. Cartis, N.I.M. Gould and Ph.L. Toint On the oracle complexity of first-order and derivative-free algorithms for smooth nonconvex minimization Technical Report ERGO 10-005, School of Mathematics.
Published in SIAM Journal on Optimization.

C. Cartis, N.I.M. Gould and Ph.L. Toint Evaluation complexity of adaptive cubic regularization methods for convex unconstrained optimization Technical Report ERGO 10-006, School of Mathematics.
Published in Optimization Methods and Software.

C. Cartis, N.I.M. Gould and Ph.L. Toint Complexity bounds for second-order optimality in unconstrained optimization Technical Report ERGO 10-007, School of Mathematics.
To appear in Journal of Complexity.

A. Grothey and X. Yang Approximate dynamic programming with Bézier curves/surfaces for top-percentile traffic routing Technical Report ERGO 10-008, School of Mathematics.
To appear in European Journal of Operations Research.

R. Paulavičius, J. Žilinskas and A. Grothey Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds Technical Report, School of Mathematics.
Published in Optimization Letters.

2009

K. Woodsend and J. Gondzio Hybrid MPI/OpenMP parallel support vector machine training Technical Report ERGO 09-001, School of Mathematics.
Published in Journal of Machine Learning Research.

X. Yang, J. Gondzio and A. Grothey Asset-Liability Management Modelling with Risk Control by Stochastic Dominance Technical Report ERGO 09-002, School of Mathematics.
Published in Journal of Asset Management.

M. Colombo, A. Grothey, J. Hogg, K. Woodsend and J. Gondzio A structure-conveying modelling language for mathematical and stochastic programming Technical Report ERGO 09-003, School of Mathematics.
Published in Mathematical Programming Computation.

C. Cartis, N.I.M. Gould and Ph.L. Toint An adaptive cubic regularisation algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity Technical Report ERGO 09-004, School of Mathematics.
Published in IMA Journal of Numerical Analysis.

J.D. Blanchard, C. Cartis and J. Tanner Compressed sensing: how sharp is the restricted isometry property? Technical Report ERGO 09-005, School of Mathematics.

A. Grothey and X. Yang Top percentile traffic routing by dynamic programming Technical Report ERGO 09-006, School of Mathematics.
To appear in Optimization and Engineering.

M. Colombo and A. Grothey A multi-step interior point warm-start approach for large-scale stochastic linear programming Technical Report ERGO 09-007, School of Mathematics.

M. Colombo and A. Grothey A decomposition-based warm-start method for stochastic programming Technical Report ERGO 09-008, School of Mathematics.

S. Bellavia, J. Gondzio and B. Morini Computational experience with numerical methods for nonnegative least-squares problems Technical Report ERGO 09-009, School of Mathematics.
Published in Numerical Linear Algebra with Applications.

J.D. Blanchard, C. Cartis, J. Tanner and A. Thompson Phase transitions for greedy sparse approximation algorithms Technical Report ERGO 09-010, School of Mathematics.

J.D. Blanchard and A. Thompson On support sizes of restricted isometry constants Technical Report ERGO 09-011, School of Mathematics.

J. Gondzio Matrix-free interior point method Technical Report ERGO 09-012, School of Mathematics.
Published in Computational Optimization and Applications.

C. Cartis, N.I.M. Gould and Ph.L. Toint On the complexity of steepest descent, Newton's and regularized Newton's methods for nonconvex unconstrained optimization Technical Report ERGO 09-013, School of Mathematics.
Published in SIAM Journal on Optimization.

R. Fletcher A limited memory steepest descent method Technical Report ERGO 09-014, School of Mathematics.

A. Grothey Financial applications: parallel portfolio optimization Book Chapter, School of Mathematics.
Published in Parallel Computing: Numerics, Applications, and Trends, Springer.

2008

C. Cartis, N.I.M. Gould and Ph.L. Toint Trust-region and other regularisations of linear least-squares problems Technical Report ERGO 08-001, School of Mathematics.

H. Du, P.-J. Chung, J. Gondzio and B. Mulgrew Robust transmit beamforming based on probabilistic constraint Technical Report ERGO 08-002, School of Mathematics.

P.-J. Chung, H. Du and J. Gondzio A probabilistic constraint approach for robust transmit beamforming with imperfect channel information Technical Report ERGO 08-003, School of Mathematics.

S. Bellavia, C. Cartis, N.I.M. Gould, B. Morini, Ph.L. Toint Convergence of a Regularized Euclidean Residual algorithm for nonlinear least-squares Technical Report ERGO 08-004, School of Mathematics.

2007

J.A.J. Hall Towards a practical parallelisation of the simplex method Technical Report, School of Mathematics.
Published in Computational Management Science.

E. Fragnière, J. Gondzio and X. Yang Operations risk management by planning optimally the qualified workforce capacity Technical Report MS 07-001, School of Mathematics.
Published in European Journal of Operational Research.

K. Woodsend and J. Gondzio Exploiting separability in large scale linear support vector machine training Technical Report MS 07-002, School of Mathematics.
Published in Computational Optimization and Applications.

G. Al-Jeiroudi and J. Gondzio Convergence analysis of inexact infeasible interior point method for linear optimization Technical Report MS 07-003, School of Mathematics.
Published in Journal of Optimization Theory and Applications.

S. Bellavia, J. Gondzio and B. Morini Regularization and preconditioning of KKT systems arising in nonnegative least-squares problems Technical Report MS 07-004, School of Mathematics.
Published in Numerical Linear Algebra with Applications.

A. Pagès, J. Gondzio and N. Nabona Warmstarting for interior point methods applied to the long-term power planning Technical Report MS 07-005, School of Mathematics.
Published in European Journal of Operational Research.

C. Cartis, N.I.M. Gould and Ph.L. Toint Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results Technical Report MS 07-006, School of Mathematics.
Published in Mathematical Programming.

J.S. Dagpunar Simulation and Monte Carlo: With applications in Finance and MCMC John Wiley and Sons, Chichester.

J.S. Dagpunar Novel Importance sampling for the valuation of Basket and Asian Options Technical report, School of Mathematics.

K. Woodsend and J. Gondzio Parallel support vector machine training with nonlinear kernels Technical Report MS 07-007, School of Mathematics.

C. Cartis, N.I.M. Gould and Ph.L. Toint Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity Technical Report MS 07-008, School of Mathematics.
Published in Mathematical Programming.

2006

J. Gondzio and A. Grothey Solving distribution planning problems with the interior point method Technical Report MS 06-001, School of Mathematics.

G. Al-Jeiroudi, J. Gondzio and J.A.J. Hall Preconditioning indefinite systems in interior point method for large scale linear optimization Technical Report MS 06-003, School of Mathematics.
Published in Optimization Methods and Software.

M. Colombo, J. Gondzio and A. Grothey A warm-start approach for large-scale stochastic linear programs Technical Report MS 06-004, School of Mathematics.
Published in Mathematical Programming.

J. Gondzio and A. Grothey A new unblocking technique to warmstart interior point methods based on sensitivity analysis Technical Report MS 06-005, School of Mathematics.
Published in SIAM Journal on Optimization.

J. Gondzio and A. Grothey Solving nonlinear financial planning problems with 10⁹ decision variables on massively parallel architectures Published in Computational Finance and its Applications II, WIT Transactions on Modelling and Simulation.

2005

J.A.J. Hall Towards a practical parallelisation of the simplex method Technical Report, School of Mathematics.

M. Colombo and J. Gondzio Further development of multiple centrality correctors for interior point methods Technical Report MS 05-001, School of Mathematics.
Published in Computational Optimization and Applications.

L. Bergamaschi, J. Gondzio, M. Venturin and G. Zilli Inexact constraint preconditioners for linear systems arising in interior point methods Technical Report MS 05-002, School of Mathematics.
Published in Computational Optimization and Applications.

J. Gondzio and A. Grothey Direct solution of linear systems of size 10⁹ arising in optimization with interior point methods Technical Report MS 05-003, School of Mathematics.
Published in Lecture Notes in Computer Science.

2004

J. Gondzio and A. Grothey Solving nonlinear portfolio optimization problems with the primal-dual interior point method Technical Report MS 04-001, School of Mathematics.
Published in European Journal of Operational Research.

F.P. Ganneau, F.J. Ulm, J. Gondzio and E.J.Garboczi An algorithm for computing the compressive strength of heterogeneous cohesive-frictional materials - Application to cement paste Published in Computers and Geotechnics.

J. Gondzio and A. Grothey Exploiting structure in parallel implementation of interior point methods for optimization Technical Report MS 04-004, School of Mathematics.
Published in Computational Management Science.

2003

J. Gondzio and A. Grothey Parallel interior point solver for structured quadratic programs: application to financial planning problems Technical Report MS 03-001, School of Mathematics.
Published in Annals of Operations Research.

J. Filar, J. Gondzio and V. Ejov An interior point heuristic for the Hamiltonian Cycle Problem via Markov decision processes Technical Report, School of Mathematics, The University of South Australia.
Published in Journal of Global Optimization.

J. Ansell, T. Archibald, J. Dagpunar, L. Thomas, P. Abell, D. Duncalf Analysing maintenance data to gain insight into systems performance Published in Journal of the Operational Research Society.

2002

A. Grothey A second order trust region bundle method for nonconvex nonsmooth optimization Technical Report MS 02-001, School of Mathematics.

L. Bergamaschi, J. Gondzio and G. Zilli Preconditioning indefinite systems in interior point methods for optimization Technical Report MS 02-002, School of Mathematics.
Published in Computational Optimization and Applications.

J.A.J. Hall and K.I.M. McKinnon Hyper-sparsity in the revised simplex method and how to exploit it Technical Report, School of Mathematics.
Published in Computational Optimization and Applications.

2001

J. Gondzio and A. Grothey Reoptimization with the primal-dual interior point method Technical Report MS 01-004, Department of Mathematics and Statistics.
Published in SIAM Journal on Optimization.

J. Ansell, T. Archibald, J. Dagpunar, L. Thomas, P. Abell, D. Duncalf Assessing the maintenance in a process using a semi-parametric approach Published in Quality and Reliability Engineering International.

2000

O. Epelly, J. Gondzio and J.-P. Vial An interior point solver for smooth convex optimization with an application to environmental-energy-economic models Logilab Technical Report, Department of Management Studies, University of Geneva.

J. Gondzio, R. Kouwenberg and T. Vorst Hedging options under transaction costs and stochastic volatility Technical Report MS 00-004, Department of Mathematics and Statistics.
Published in Journal of Economic Dynamics and Control.

A. Grothey and K.I.M. McKinnon Decomposing the optimization of a gas lifted oil well network Technical Report MS 00-005, Department of Mathematics and Statistics.

J.A.J. Hall and K.I.M. McKinnon Hyper-sparsity in the revised simplex method and how to exploit it Technical Report MS 00-015, Department of Mathematics and Statistics.

Xiaoling Sun, K.I.M. McKinnon and Duan Li A convexification method for a class of global optimization problems with applications to reliability optimization Technical Report MS 00-017, Department of Mathematics and Statistics.
Published in Journal of Global Optimization.

Duan Li, Xiaoling Sun and K.I.M. McKinnon An exact solution method for reliability optimization in complex systems Technical Report MS 00-018, Department of Mathematics and Statistics.

J. Gondzio and R. Sarkissian Parallel interior point solver for structured linear programs Technical Report MS 00-025, Department of Mathematics and Statistics.
Published in Mathematical Programming.

1999

J. Gondzio and R. Kouwenberg High performance computing for asset liability management Technical Report MS 99-004, Department of Mathematics and Statistics.
Published in Operations Research.

A. Grothey, S. Leyffer and K.I.M. McKinnon A note on feasibility in Benders decomposition Numerical Analysis Report NA/188, University of Dundee.

J.A.J. Hall and K.I.M. McKinnon Exploiting hyper-sparsity in the revised simplex method Technical Report MS 99-014, Department of Mathematics and Statistics.

1998

J. Gondzio, R. Sarkissian and J.-P. Vial Parallel implementation of a central decomposition method for solving large scale planning problems HEC Technical Report 98.1 , Department of Management Studies, University of Geneva.
Published in Computational Optimization and Applications.

A. Altman and J. Gondzio Regularized symmetric indefinite systems in interior point methods for linear and quadratic optimization HEC Technical Report 98.6, Department of Management Studies, University of Geneva.
Published in Optimization Methods and Software.

E. Fragnière, J. Gondzio and R. Sarkissian Efficient management of multiple sets to extract complex structures from mathematical programs Logilab Technical Report, Department of Management Studies, University of Geneva.
Published in Annals of Operations Research.

E. Fragnière, J. Gondzio and J.-P. Vial Building and solving large-scale stochastic programs on an affordable distributed computing system Logilab Technical Report 98.11, Department of Management Studies, University of Geneva.
Published in Annals of Operations Research.

A. Grothey and K.I.M. McKinnon A superlinearly convergent trust region bundle method Technical Report MS98-015, Departments of Mathematics and Statistics.

1997

J. Gondzio and J.-P. Vial Warm start and epsilon-subgradients in the cutting plane scheme for block-angular linear programs Logilab Technical Report 97.1, Department of Management Studies, University of Geneva.
Published in Computational Optimization and Applications.

E. Fragnière, J. Gondzio, R. Sarkissian and J.-P. Vial Structure exploiting tool in algebraic modeling languages Logilab Technical Report 97.2, Department of Management Studies, University of Geneva.
Published in Management Science.

1996

T.W. Archibald, C.S. Buchanan, K.I.M. McKinnon and L.C. Thomas Nested Benders decomposition and dynamic programming for reservoir optimization Technical Report MS 96-001, Department of Mathematics and Statistics.

S. Berner, K.I.M. McKinnon and C. Millar A parallel algorithm for the global minimization of Gibbs free energy Technical Report MS 96-004, Department of Mathematics and Statistics.
Published in Annals of Operations Research.

K.I.M. McKinnon Convergence of the Nelder-Mead simplex method to a non-stationary point Technical Report MS 96-006, Department of Mathematics and Statistics.
Published in SIAM Journal on Optimization.

J.A.J. Hall and K.I.M. McKinnon The simplest examples where the simplex method cycles and conditions where EXPAND fails to prevent cycling Technical Report MS 96-010, Department of Mathematics and Statistics.
Published in Mathematical Programming.

K.I.M. McKinnon and M. Mongeau A generic global optimization algorithm for the chemical and phase equilibrium problem Technical Report MS 96-011, Department of Mathematics and Statistics.
Published in Journal of Global Optimization.

J.A.J. Hall and K.I.M. McKinnon PARSMI, a parallel revised simplex algorithm incorporating minor iterations and Devex pricing Technical Report MS 96-012, Department of Mathematics and Statistics.
Published in Springer Lecture Notes in Computer Science.

T.W. Archibald, K.I.M. McKinnon and L.C. Thomas An aggregate stochastic dynamic programming model of multi-reservoir systems Technical Report MS 96-018, Department of Mathematics and Statistics.
Published in Water Resources Research.

J. Gondzio Warm start of the primal-dual method applied in the cutting plane scheme Logilab Technical Report 96.3, Department of Management Studies, University of Geneva.
Published in Mathematical Programming.

J. Gondzio and R. Sarkissian Column generation with a primal-dual method Logilab Technical Report 96.6, Department of Management Studies, University of Geneva.