An extension of the simplex algorithm is presented. For a given linear programming problem, a sequence of relaxed linear programming problems is solved until a solution to the original problem is reached. Each successive relaxed problem is obtained from the previous one by adding a single constraint chosen from the constraints violated by the solution to the previous relaxed problem. This added...

Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generali...

In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is n...

In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints, the number of variables, and the ratio between the minimum and the maximum values of all the positive elements of primal basic feasible solutions. When the ...

An active area of research for linear programming is to construct initial Simplex tableau that is close to the optimal solution, and to improve its pivoting selection strategies efficiently. In this paper, we present a new approach to the problem of initialization and pivoting rules: the algorithm is free from any artificial variables and artificial constraints, known as the big-M methods. By s...

In this paper, a parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen as a variant of the multi-objective simplex (Evans-Steuer) algorithm [12]. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a solution in the sense of Lö...

A hybrid search method based on Ant Colony Optimization for Continuous Domains ( ACO ) and the Nelder-Mead Simplex algorithm is proposed to calculate the stability margin of linear time-invariant time-delay systems. The effectiveness of the Nelder-Mead Simplex procedure is combined with the global search power of the ACO method to obtain the stability margin of linear timeinvariant time-delay s...

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...

We consider the subclass of linear programs that formulate Markov Decision Processes (mdps). We show that the Simplex algorithm with the GassSaaty shadow-vertex pivoting rule is strongly polynomial for a subclass of mdps, called controlled random walks (CRWs); the running time is O(|S| · |U |), where |S| denotes the number of states and |U | denotes the number of actions per state. This result ...

Our research is motivated by the simplex algorithm for linear programming. We consider the variation where the algorithm chooses at each step the next position uniformly at random from all improving neighbouring positions; this rule is commonly called Random-Edge. Its expected runtime on general linear programs can be mildly exponential; cf. Friedmann et al. [2011]. Better bounds can be hoped f...