Mathematical developments arising from linear programming, Proc. AMS-IMS- SIAM Jt. Summer Res. Conf., Brunswick/ME (USA) 1988, Contemp. Math. 114, 91-107 (1990).
Summary: [For the entire collection see Zbl 0722.00047.]
We describe a primal-dual potential function for linear programming
where , x is the primal variable and s is the dual-slack variable in the standard linear programming form. As a result, we develop an interior algorithm seeking reductions in the potential function with . The algorithm neither traces the central path nor uses projective transformations. It converges to the optimal solution set in O( iterations and uses arithmetic operations.