  The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a
novel iterative algorithm to solve linear programming problems. A symplex
pivoting operation is simply an exchange between a basic variable and a
non-basic variable, in the Goldman-Tucker Compact-Symmetric-Tableau (CST) which
is a unique symmetric representation common to both the primal as well as the
dual of a linear programming problem in its standard canonical form. From this
viewpoint, the classical simplex pivoting operation of Dantzig may be
considered as a restricted special case.
  The infeasibility index associated with a symplex tableau is defined as the
sum of the number of primal variables and the number of dual variables that are
infeasible. A measure of goodness as a global effectiveness measure of a pivot
selection is defined/determined as/by the decrease in the infeasibility index
associated with such a pivot selection. The selection of the symplex pivot
element is made by seeking the best possible anticipated decrease in the
infeasibility index from among a wide range of candidate choices with non-zero
values - limited only by considerations of potential numerical instability.
After passing through a non-repeating sequence of CST tableaus, the algorithm
terminates when further reduction in the infeasibility index is not possible;
then the tableau is checked for the terminal tableau type to facilitate the
problem classification - a termination with an infeasibility index of zero
indicates optimum solution. Even in the absence of an optimum solution, the
versatility of the spdspds algorithm allows one to explore/determine the most
suitable alternative solutions, including possibly a comprehensive parametric
analysis, etc. The worst-case computational complexity of the spdspds algorithm
is shown to be $O(L^{1.5})$ where L is the problem-size expressed in terms of
the size(length) of the input data.

Optimization and Control