A projective simplex method for linear programming

The (Dantzig) simplex method for linear programming

G eorge Dantzig, in describing the " Origins of the Simplex Method, " 1 noted that it was the availability of early digital computers that supported and invited the development of LP models to solve real-world problems. He agreed that invention is sometimes the mother of necessity. Moreover, he commented that he initially rejected the simplex method because it seemed intuitively more attractive...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems

A Dual Interior Primal Simplex Method for Linear Programming

This paper proposes a hybrid computational method (DIPS method) which works as a simplex method for solving a standard form linear program, and, simultaneously, as an interior point method for solving its dual. The DIPS method generates a sequence of primal basic feasible solutions and a sequence of dual interior feasible solutions interdependently. Along the sequences, the duality gap decrease...

An Asymptotic Simplex Method for Parametric Linear Programming

We study singularly perturbed linear programs. These are parametric linear programs whose constraints become linearly dependent when the perturbation parameter goes to zero. Problems like that were studied by Jeroslow in 1970’s. He proposed simplex-like method, which works over the field of rational functions. Here we develop an alternative asymptotic simplex method based on Laurent series expa...

A Nonstandard Simplex Algorithm for Linear Programming

The simplex algorithm travels, on the underlying polyhedron, from vertex to vertex until reaching an optimal vertex. With the same simplex framework, the proposed algorithm generates a series of feasible points (which are not necessarily vertices). In particular, it is exactly an interior point algorithm if the initial point used is interior. Computational experiments show that the algorithm ar...