《《2016 Interior-point linear programming algorithm for auction methods》.pdf

572 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 15, NO. 2, MAY 2000 Interior-Point Linear Programming Algorithm for Auction Methods Somgiat Dekrajangpetch, Student Member, IEEE, and Gerald B. Sheblé, Fellow, IEEE Abstract—Interior-point programming (IP) has been applied recovery method described in [9] was that it was computation- to many power system problems because of its efficiency for big ally expensive. In experiments Marsten et al. [9] pointed out that problems. This paper illustrates application of interior-point linear recovery of an optimal basis could require more execution time programming (IPLP) to auction methods. An extended algorithm of IPLP is developed and used in this paper. This extended IPLP than was required to solve the problem by dual affine method. algorithm can find the exact optimal solution (i.e., exact optimal Megiddo [11] showed a strongly polynomial time algorithm that vertex) and can recover the optimal basis. Sensitivity analysis can found an optimal basis when any pair of optimal solutions for be performed after the optimal basis is found. The sensitivity anal- the primal and dual problems was given. This optimal basis was ysis performed in this paper is increase in bid’s price and increase optimal for both the primal and dual problems. Ye [12] devel- in flow limit of transmission line. This extended algorithm is ex- panded from the affine-scaling primal algorithm. The concept used oped a termination procedure that was guaranteed to find an in this extended algorithm to find the optimal vertex and optimal exact solution on the optimal face in a finite time. Ponnambalem basis is simple.