• Publications
  • Influence
Multiple centrality corrections in a primal-dual method for linear programming
  • J. Gondzio
  • Mathematics, Computer Science
  • Comput. Optim. Appl.
  • 1 September 1996
TLDR
A modification of the (infeasible) primal-dual interior point method that uses multiple corrections to improve the centrality of the current iterate and gives on the average a 25% to 40% reduction in the number of iterations compared with the widely used second-order predictor-corrector method. Expand
Interior point methods 25 years later
  • J. Gondzio
  • Mathematics, Computer Science
  • Eur. J. Oper. Res.
  • 1 May 2012
TLDR
Interior point methods for linear and (convex) quadratic programming display several features which make them particularly attractive for very large scale optimization, including their low-degree polynomial worst-case complexity and an unrivalled ability to deliver optimal solutions in an almost constant number of iterations. Expand
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
TLDR
Two types of preconditioners which use some form of incomplete Cholesky factorization for indefinite systems are proposed in this paper, and it is revealed that the solution times for such problems on a modern PC are measured in minutes when direct methods are used and drop to seconds when iterative methods with appropriate preconditionsers are used. Expand
HOPDM (version 2.12) — A fast LP solver based on a primal-dual interior point method
HOPDM is an implementation of the primal-dual interior point method for solving large scale linear programming (LP) problems. HOPDM stands for Higher Order Primal Dual Method. Its newest version 2.12Expand
Implementation of Interior Point Methods for Large Scale Linear Programming
TLDR
An overview of the most important characteristics of advanced implementations of interior point methods is given. Expand
Regularized Symmetric Indefinite Systems in Interior Point Methods for Linear and Quadratic Optimization
This paper presents linear algebra techniques used in the implementation of an interior point method for solving linear programs and convex quadratic programs with linear constraint. The newExpand
Parallel interior-point solver for structured linear programs
TLDR
The solver allows a nested embedding of structures and by this means very complicated real-life optimization problems can be modelled and the efficiency of the solver is illustrated on several problems arising in the optimization of networks. Expand
Matrix-free interior point method
  • J. Gondzio
  • Mathematics, Computer Science
  • Comput. Optim. Appl.
  • 1 March 2012
TLDR
A redesign of a linear algebra kernel of an interior point method to avoid the explicit use of problem matrices is presented and preliminary computational results for small problems limited to 1 million of variables and 10 million of nonzero elements demonstrate the feasibility of the approach. Expand
Further development of multiple centrality correctors for interior point methods
TLDR
Through extensive numerical experience, it is shown that the proposed centrality correcting scheme leads to noteworthy savings over second-order predictor–corrector technique and previous implementations of multiple centrality correctors. Expand
Warm start of the primal-dual method applied in the cutting-plane scheme
  • J. Gondzio
  • Mathematics, Computer Science
  • Math. Program.
  • 1 September 1998
A practical warm-start procedure is described for the infeasible primal-dual interior-point method (IPM) employed to solve the restricted master problem within the cutting-plane method. In contrastExpand
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