The group has a strong experience in research and development of computational techniques. This is reflected in the production and implementation of computational software.

24 parallel sparse PCA codes based on alternating maximization by Peter Richtárik and Martin Takáč.

Accelerated coordinate descent methods for minimizing composite functions by Peter Richtárik and Martin Takáč.

*BASICLU* implements a sparse LU factorization and an update method
that maintains the factorization after column changes to the matrix. It is
intended for use in simplex-type algorithms and has been tailored to
hypersparse linear programming problems.

The algorithm is described in Technical Report ERGO 17-002 and the source code is available from the ERGO github page.

HiGHS is a high performance serial and parallel solver for large scale sparse linear programming problems.

HiGHS is based on research which has yielded best paper prizes for 2005, 2015 and 2018. The source code is available from the ERGO github page.

*LURank* is an implementation of an LU factorization which reveals
the rank of the matrix. It applies the maximum volume concept when performing
Gaussian elimination.

*HOPDM* (Higher Order Primal-Dual Method) is Jacek Gondzio's
implementation of an infeasible primal-dual path-following interior point
method for linear, convex quadratic and convex nonlinear programming
problems.

HOPDM allows solving large scale linear, convex quadratic and convex nonlinear programming problems. The code algorithm uses multiple centrality correctors; their number is chosen appropriately for a given problem in order to reduce the overall solution time. HOPDM automatically chooses the most efficient factorization method for a given problem (either normal equations or augmented system). The code compares favourably with commercial LP, QP and NLP packages.

*IPX* implements a linear programming interior point solver based
on iterative linear algebra. It provides a crossover method for recovering
a basic solution. The algorithm is described in
Technical Report ERGO 18-014 and the source code is
available from the ERGO github
page.

*MFIPMCS* (Matrix-free Interior Point Method for Compressed Sensing)
is an interior point method implemented in MATLAB for the solution of real
valued compressed sensing problems.

The "matrix-free" implies that only matrix-vector products operations are allowed and the process is memoryless. The solver employs an efficient preconditioning technique along with a Krylov subspace method (i.e conjugate gradient) for the fast solution of linear systems at every iteration.

More information about MFIPMCS

*OOPS* (Object-Oriented Parallel Solver) is a parallel interior point
code that exploits any special structure in the Hessian and Jacobian matrices,
developed by Jacek Gondzio, Andreas Grothey and Robert Sarkissian.

The solver is an implementation of the primal-dual interior point method with multiple centrality correctors. The solver is implemented using object-oriented programming techniques. It solves linear (LP), quadratic (QP) and nonlinear (NLP) problems. The sequential code compares favourably with commercial packages and the parallel code shows perfect speed-ups.

*pdNCG* (primal-dual Newton Conjugate Gradients) is a MATLAB
implementation for the solution of L1-regularized strongly-convex problems.
The solver is memoryless, it requires only matrix-vector product operations,
hence it is appropriate for large-scale instances.

*S2GD* is an efficient implementation of Semi Stochastic Gradient
Descent for logistic regression by Jakub Konečný.

*SML* (Structured Modelling Language) is an implementation of a
structure-conveying extension to the AMPL modelling language.

SML extends AMPL with object-oriented features that allow to construct models from sub-models. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Its design allows the problem generation phase to be parallelisable.

*SVM-OOPS*, developed by Kristian Woodsend and Jacek Gondzio,
is for training standard linear support vector machines. It uses the
*OOPS* solver, and incorporates SVM reformulations designed for
interior point methods.

The algorithm is best suited for large-scale classification problems, where the number of samples greatly exceeds the number of features. It is highly efficient on multicore processors, solving problems involving tens or hundreds of thousands of support vectors. Larger problems can be solved on computing clusters using a combination of OpenMP and MPI. Our approach has the additional benefit of providing a good early approximation to the separating hyperplane.

More information about SVM-OOPS

Instance generators for l1-regularized over- and underdetermined least squares, written by Kimon Fountoulakis and Jacek Gondzio.