151. An Algorithm for Solving Linear Programming Problems in O(n 3 L) Operations
- Author
-
Clovis C. Gonzaga
- Subjects
Hessian matrix ,Linear programming ,MathematicsofComputing_NUMERICALANALYSIS ,Linear-fractional programming ,symbols.namesake ,Simplex algorithm ,symbols ,Karmarkar's algorithm ,Second-order cone programming ,Penalty method ,Criss-cross algorithm ,Hardware_ARITHMETICANDLOGICSTRUCTURES ,Algorithm ,Mathematics - 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.
- Published
- 1989
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