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

Clovis C. Gonzaga

Chapter Chapter 1 in Progress in Mathematical Programming, 1989, pp 1-28 from Springer

Abstract: 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.

Keywords: Barrier Function; Linear Programming Problem; Projection Matrix; Quadratic Approximation; Hessian Matrice (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4613-9617-8_1

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