A little bit of reflection should convince you that the present scenario is essentially the same as that at the start of Phase II of the standard Simplex method. There is, however, a logistical difference, namely that the standard Simplex tableau associated with the current solution is not explicitly available to us. Therefore, we need to develop a different set of procedures for generating inf...

The paper presents an approach for avoiding and minimizing the complementary pivots in a simplex based solution method for a quadratic programming problem. The linearization of the problem is slightly changed so that the simplex or interior point methods can solve with full speed. This is a big advantage as a complementary pivot algorithm will take roughly eight times as longer time to solve a ...

This work describes the minimum volume enclosing simplex problem, which is known to be a multimodal Global Optimization problem. The problem has been used as a basis to estimate so-called endmember and abundance data in unmixing spectral data of hyperspectral sensors. This estimation problem is a big challenge. We explore the possibility of a new estimation algorithm using the minimum volume en...

We propose an algorithm for dimensionality reduction on the simplex, mapping a set of high-dimensional distributions to a space of lower-dimensional distributions, whilst approximately preserving pairwise Hellinger distance between distributions. By introducing a restriction on the input data to distributions that are in some sense quite smooth, we can map n points on the d-simplex to the simpl...

This study reports on optimization of the RP-HPLC separation of imidazolium and pyridinium ionic liquid cations using a variable-size simplex algorithm. Under the optimized conditions, all critical pairs of ionic liquids were successfully separated in a single chromatographic run. The mobile phase at the point corresponding to the optimum consisted of 10% MeOH and 90% 15 mM KH(2)PO(4)/H(3)PO(4)...

The authors recently proposed a simplex-based Tardos’ algorithm which is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate. Motivated by the algorithmic practically of such methods, we introduce a modification which circumvents the determination of the largest sub-determinant while keeping the same theoretical performance. Assuming...

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel and combines the dual solutions to obtain a new d...

We report a remarkable success of nested pricing rules over major pivot rules commonly used in practice, such as Dantzig’s original rule as well as the steepest-edge rule and Devex rule.

We investigate the worst-case behavior of the simplex algorithm on linear programs with 3 variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the “random edge” rule yields the best asymptotic behavior as well as the most complicated analysis. All other rules turn out to be much easier to study, but also produce worse results: Most of them show essentia...

The wind turbine power decreases at low speed. A flanged diffuser plays a role of device for collecting and accelerating the approaching wind, thus optimization shape presents an important way to enhance power. In this work, numerical parametric study was conducted on obtain initial optimum form diffuser. Then, Simplex algorithm is used optimal starting from obtained shape. Finally, with conven...