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An Algorithm for Solving Linear Programming Problems in O(n 3 L) Operations

In: Progress in Mathematical Programming

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  • Clovis C. Gonzaga

Abstract

This chapter describes a short-step penalty function algorithm that solves linear programming problems in no more than O(n 0.5 L) iterations. The total number of arithmetic operations is bounded by O(n 3 L), carried on with the same precision as that in Karmarkar’s algorithm. Each iteration updates a penalty multiplier and solves a Newton-Raphson iteration on the traditional logarithmic barrier function using approximated Hessian matrices. The resulting sequence follows the path of optimal solutions for the penalized functions as in a predictor-corrector homotopy algorithm.

Suggested Citation

  • Clovis C. Gonzaga, 1989. "An Algorithm for Solving Linear Programming Problems in O(n 3 L) Operations," Springer Books, in: Nimrod Megiddo (ed.), Progress in Mathematical Programming, chapter 0, pages 1-28, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-9617-8_1
    DOI: 10.1007/978-1-4613-9617-8_1
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