Combining interior-point and pivoting algorithms for linear programming

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:35765

Anderson, E; Ye, Y

In this paper we propose a new approach to combine linear programming (LP) interior-point and simplex pivoting algorithms. We present a strongly polynomial procedure, similar to Megiddo`s, in any iteration of an interior-point algorithm to produce a basis. We show that this basis will eventually become optimal after a finite number of interior-point iterations. Our combined method naturally handles the case where the interior-point algorithm does not provide an exact optimal or feasible solution. In fact, our method allows either cross over to the simplex algorithm or to execute the two algorithms alternately. Furthermore, if LP data are rational, the total number of pivoting steps to generate an optimal basis can be bounded above by O(n{radical}n L), where L is the data size and n is the number of variables in the standard primal form. We also report encouraging computational results for this combined approach.

• OSTI ID: 35765
• Report Number(s): CONF-9408161--
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CONVERGENCE
EFFICIENCY
LINEAR PROGRAMMING
NUMERICAL SOLUTION