Handling dense columns in Interior-Point Methods

Autores

  • Catalina J. Villalba
  • Aurelio R.L. Oliveira

DOI:

https://doi.org/10.5540/03.2023.010.01.0060

Palavras-chave:

Linear programming, Interior-point methods, Preconditioner

Resumo

The Interior-Point methods are a type of method used to solve linear programming problems that require solving linear systems. In situations where the constraint matrix has dense columns, it is essential to find an efficient way to solve computationally these systems in order to avoid memory issues or increase the number of operations. This project proposes a precondi- tioner to handle this issue, and it provides both theoretical predictions and computational tests to demonstrate its effectiveness.

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Biografia do Autor

Catalina J. Villalba

UNICAMP, Campinas, SP

Aurelio R.L. Oliveira

UNICAMP, Campinas, SP

Referências

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D. Goldfarb and K. Scheinberg. “A product-form Cholesky factorization method for handling dense columns in interior point methods for linear programming”. In: Mathematical Programming 99.1 (2004), pp. 1–34. doi: 10.1007/s10107-003-0377-7.

J. Gondzio. “Interior point methods 25 years later”. In: European Journal of Operational Research 218.3 (2012), pp. 587–601. doi: 10.1016/j.ejor.2011.09.017.

J. Gondzio. “Splitting dense columns of constraint matrix in interior point methods for large scale linear programming”. In: Optimization 24.3-4 (1992), pp. 285–297. doi: 10.108/02331939208843796.

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R. J. Vanderbei. “Splitting dense columns in sparse linear systems”. In: Linear Algebra and its Applications 152 (1991), pp. 107–117. doi: 10.1016/0024-3795(91)90269-3.

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Publicado

2023-12-18

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