K-Sum Linear Programming
提出K和线性规划问题,它包含经典线性规划和极小化极大线性规划,并证明可在多项式时间内求解,还给出了两种基于单纯形的算法。
In this note we introduce the k-sum linear programming problem (KLP) which subsumes the classical linear programming problem and the minmax linear programming problem. KLP can be transformed into a linear program with an exponential number of additional constraints and one additional variable. Exploiting the special structure of these additional constraints, we show that KLP can be solved in polynomial time. Two promising simplex-based algorithms are also suggested to solve KLP.