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Full-Text Articles in Physical Sciences and Mathematics
Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder
Simultaneous Data Perturbations And Analytic Center Convergence, Allen G. Holder
Mathematics Faculty Research
The central path is an infinitely smooth parameterization of the non-negative real line, and its convergence properties have been investigated since the middle 1980s. However, the central "path" followed by an infeasible-interior-point method relies on three parameters instead of one, and is hence a surface instead of a path. The additional parameters are included to allow for simultaneous perturbations in the cost and righ-hand side vectors. This paper provides a detailed analysis of the perturbed central path that is followed by infeasible-interior-point methods, and we characterize when such a path converges. We develop a set (Hausdorff) convergence property and show …
An Extension Of The Fundamental Theorem Of Linear Programming, A Brown, A Gedlaman, Allen G. Holder, S Martinez
An Extension Of The Fundamental Theorem Of Linear Programming, A Brown, A Gedlaman, Allen G. Holder, S Martinez
Mathematics Faculty Research
In 1947 George Dantzig developed the Simplex Algorithm for linear programming, and in doing so became known as The Father of Linear Programming. The invention of the Simplex Algorithm has been called "one of the most important discoveries of the 20th century," and linear programming techniques have proven useful in numerous fields of study. As such, topics in linear optimization are taught in a variety of disciplines. The finite convergence of the simplex algorithm hinges on a result stating that every linear program with an optimal solution has a basic optimal solution; a result known as the Fundamental Theorem of …