The simplex algorithm requires artificial variables for solving linear programs, which lack primal feasibility at the origin point. We present a new general-purpose solution algorithm, called Push-and-Pull, which obviates the use of artificial variables. The algorithm consists of preliminaries for setting up the initialization followed by two main phases. The Push Phase develops a basic variabl...

In this paper, based on our previous research on simplex genetic algorithm, we put forward an adaptive approach for the self-adaptation of the percentage of simplex. According to the average fitness of those individuals generated by simplex operator in a certain generation, a set of rules is designed to adaptively adjust the simplex percentage within a certain range. This helps the algorithm al...

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...

We develop a tropical analogue of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m + n)) time, where m is the number of constraints and n is the dimension.

in the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. in the second part we discuss some recent developments concurring the simplex algorithm. we describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.

network environments always can be invaded by intruder agents. in networks where nodes are performing some computations, intruder agents might contaminate some nodes. therefore, problem of decontaminating a network infected by intruder agents is one of the major problems in these networks. in this paper, we present a distributed asynchronous local algorithm for decontaminating a network. in mos...

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...

We have developed a new algorithm, RBF-MREIT, for Magnetic Resonance Electrical Impedance Tomography (MREIT) by applying the radial basis function (RBF) network and Simplex method. RBF-MREIT uses only one component of the measured magnetic flux density to reconstruct the conductivity images, and provides a solution to the rotation problem in MREIT. The proposed algorithm is tested on a three-sp...

The simplex algorithm was designed by Danzig in 1947. This write-up presents the main ideas involved. It is a slight update (mostly in Section 1.9) of lecture notes from 2004. In 2011 the material was covered in much less detail, and this write-up can serve as supplementary material for those students who want to know more about the simplex algorithm. Sections 1.7 and 1.8 were not discussed at ...

The dynamic tree is an abstract data type that allows the maintenance of a collection of trees subject to joining by adding edges (linking) and splitting by deleting edges (cutting), while at the same time allowing reporting of certain combinations of vertex or edge values. For many applications of dynamic trees, values must be combined along paths. For other applications, values must be combin...