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...

The present work encounters the solution of the defect identification problem with the use of an evolutionary algorithm combined with a simplex method. In more details, a Matlab implementation of Genetic Algorithms is combined with a Simplex method in order to lead to the successful identification of the defect. The influence of the location and the orientation of the depressed ellipsoidal flaw...

A lot of research has been done to 1nd a faster (polynomial) algorithm that can solve linear programming (LP) problems. The main branch of this research has been devoted to interior point methods (IPM). The IPM outperforms the Simplex method in large LPs. However, there is still much research being done in order to improve pivoting algorithms. In this paper, we present a new approach to the pro...

This paper proposes a streamlined form of simplex method which provides some great benefits over traditional simplex method. For instance, it does not need any kind of artificial variables or artificial constraints; it could start with any feasible or infeasible basis of an LP. This method follows the same pivoting sequence as of simplex phase 1 without showing any explicit description of artif...

As it is well-known, since the discovery of the interior-point methods linear programming (LP) is no longer synonymous with the celebrated simplex method. The interior-point methods (IPMs) have not only a better complexity bound than the simplex method (polynomial vs. exponential) but also enjoy practical efficiency and can be considerably faster than the simplex method for many (but not for al...

This paper studies the collaborative rating allocation problem, in which each user has limited ratings on all items. These users are termed “energy limited”. Different from existing methods which treat each rating independently, we investigate the geometric properties of a user’s rating vector, and design a matrix completion method on the simplex. In this method, a user’s rating vector is estim...

W i tzgal l [ 7 L comment ing on the gradient project ion methods of R . Frlsch and J . B . Rosen , states: "More or less a l l algori thms for solving the l inear programming problem are known to be modificat ions of an algori thm for matrix inversion . Thus the simplex method corresponds to the Gauss-Jordan method . The methods of Frisch and Rosen are based on an interest ing method for inver...

This paper presents a method for the assignment of simplex signals in a circular trellis-coded modulation (CTCM) scheme. Background is given on both CTCM and simplex signaling. The CTCM trellis is then shown to have various properties that allow symbol assignment to be carried out in a systematic manner.