We present a simplex-type algorithm for linear programming that works with primal-feasible and dual-feasible points associated with bases that di er by only one column.

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In this paper, we show that the parametric simplex method is an efficient algorithm for solving various statistical learning problems that can be written as linear programs parametrized by a so-called regularization parameter. The parametric simplex method offers significant advantages over other methods: (1) it finds the complete solution path for all values of the regularization parameter by ...

We transform a 2-dimensional second-order cone program to a standard linear program in order to pivot a vector based on its three states. Related properties of the transformation are given. Based on the transformation, we interpret the simplex method and its sensitivity analysis for the 2-dimensional second-order cone programming, especially the state changes. Finally, we give some applications...

There are two interesting methods, in the literature, for solving fuzzy linear programming problems in which the elements of coefficient matrix of the constraints are represented by real numbers and rest of the parameters are represented by symmetric trapezoidal fuzzy numbers. The first method, named as fuzzy primal simplex method, assumes an initial primal basic feasible solution is at hand. T...

Transportation problem is a linear programming which considers minimum cost for shipping a product from some origins to other destinations such as from factories to warehouse, or from a warehouse to supermarkets. To solve this problem simplex algorithmis utilized. In real projects costs and the value of supply and demands are fuzzy numbers and it is expected that optimal solutions for determini...

Signal to Noise Ratio (SNR) is an important index for wireless communications. There are many methods for increasing SNR. In CDMA systems, spreading sequences are used. We consider the frequency-selective wide-sense-stationary uncorrelated-scattering (WSSUS) channel and evaluate the worst case of SNR. We construct the non-linear programing for maximizing the lower bound of the average of SNR. T...

Although many solution methods are available for the linear programming problem, the simplex method is undoubtedly the most widely used one for its simplicity. In this paper, we propose an implementation of the simplex method on freed-size hypercubes. A partitioning technique and a mapping technique are presented to fit largo~sL~ problem instances into relatively small-size hypercubes. Two case...

In most practical problems of linear programming problems with fuzzy cost coefficients, some or all variables are restricted to lie within lower and upper bounds. In this paper, the authors propose a new method for solving such problems called the bounded fuzzy primal simplex algorithm. Some researchers used the linear programming problem with fuzzy cost coefficients as an auxiliary problem for...