In this paper, a double-pivot simplex method is proposed. Two upper bounds of iteration
numbers are derived. Applying one of the bounds to some special linear programming (LP) …

The colorful Carathéodory theorem, proved by Bárány in 1982, states that given d+ 1 sets of
points S 1,…, S d+ 1 in R d, with each S i containing 0 in its convex hull, there exists a set …

In this thesis, we present new results on the complexity of classical linear programming on
the one hand, and of tropical linear programming and mean payoff games on the other …

The colorful Carath\'eodory theorem, proved by B\'ar\'any in 1982, states that given d+ 1 sets
of points S_1,..., S_ {d+ 1} in R^ d, with each S_i containing 0 in its convex hull, there exists a …

In this paper, we consider the number of simplex iterations with the steepest-edge rule for
the simplex method. For a nondegenerate linear programming problem, we show two upper …

We obtain upper bounds for the number of distinct solutions generated by the simplex
method for linear programming (LP). One of the upper bounds is polynomial in the number …

単体法は, 線形計画問題を解く最も有名なアルゴリズムである. Klee-Minty が実際の反復回数が
指数回になり得るという否定的な研究結果を発表したことにより, 単体法の反復回数については …