A new efficient primal dual simplex algorithm

Hybrid-LP: Finding advanced starting points for simplex, and pivoting LP methods

“…The experiments of the method in Ref. [18] report running times on the order of 10 to 100 times faster when compared to both simplex and Phase I combined. In our experiments, the comparison is with the simplex method only and the Phase I procedure (which is very time consuming) is left unchanged.…”

“…[14]). Another approach is followed by the methods of Paparizzo [17], Paparizzo et al [18], and Chen et al [3], which are pivoting methods that pivot on basic solutions which are infeasible; these methods are known as exterior-point simplex.…”

Algebraic simplex initialization combined with the nonfeasible basis method

“…Stojkovic and Stanimirovic [14] used "the cosine criterion" to get an initial basis for the simplex algorithm. In 2003, Paparrizos et al [13] developed a method that starts resolution by an infeasible basis. This method involves two artificial variables and two big numbers.…”

An experimental investigation of a primal–dual exterior point simplexalgorithm

“…These advantages can be avoided if the exterior path is replaced with a dual feasible simplex path. This method has been introduced by Paparrizos et al [11]. The main idea of the Revised Primal-Dual Simplex Algorithm (RPDSA) is based on the process of moving from any interior point to an optimal basic solution.…”