On the Strictly Complementary Slackness Relation in Linear Programming

  • Shuzhong Zhang
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 1)


Balinski and Tucker introduced in 1969 a special form of optimal tableaus for LP, which can be used to construct primal and dual optimal solutions such that the complementary slackness relation holds strictly. In this paper, first we note that using a polynomial time algorithm for LP Balinski and Tucker’s tableaus are obtainable in polynomial time. Furthermore, we show that, given a pair of primal and dual optimal solutions satisfying the complementary slackness relation strictly, it is possible to find a Balinski and Tucker’s optimal tableau in strongly polynomial time. This establishes the equivalence between Balinski and Tucker’s format of optimal tableaus and a pair of primal and dual solutions to satisfy the complementary slackness relation strictly. The new algorithm is related to Megiddo’s strongly polynomial algorithm that finds an optimal tableau based on a pair of primal and dual optimal solutions.


Polynomial Time Dual Solution Optimal Basis Relative Interior Strict Complementarity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Shuzhong Zhang
    • 1
  1. 1.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands

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