The discussion centers on understanding the optimality of a point in a primal Linear Program (LP) using complementary slackness. The user presents the point x = (1,1,1,1,1,1,1) and seeks clarity on whether this point solves the primal LP. Key insights include the relationship between the primal and dual variables, particularly that if the sum of the products of the coefficients and the variables is less than the constraint b, then the corresponding dual variable y must be zero. The user expresses confusion regarding the pivoting process to derive y from x.
PREREQUISITESStudents and professionals in operations research, optimization analysts, and anyone involved in solving Linear Programming problems who seeks to deepen their understanding of primal-dual relationships and optimality conditions.
zfolwick said:I can't for the life of me understand this topic. given a point x =(1,1,1,1,1,1,1) and a primal LP, does the point solve the primal? An internet search revealed no answer to my question, only criteria which involves knowing y. I am aware that \sumaijxj < b then yi = 0, so I at least know which elements of y are zero, but the rest of the steps elude me.