Linear programming (LP) is an important tool for many inter-disciplinary optimization problems. The Simplex method is the most widely used algorithm to solve LP problems and has immense impact on several developments in various fields. With development of public domain and commercial software solvers, it has been automated and made available for use. A serious bottleneck in implementation of Si...

During the last decades a number of studies on modifications and improvement of the original algorithm have been published. The first design matrix is however one aspect of simplex optimization that has raised substantially less interest, despite the observation of its importance for the speed of convergence by Nelder and Mead. This is probably due to the fact that Spendley et al already in the...

Each year, the editorial board of computational optimization and applications (COAP) selects a paper from the preceding year’s publications for the Best Paper Award. In 2015, 92 papers were published by COAP. The recipients of the 2015 Best Paper Award are Qi Huangfu of the FICO Xpress Team and Julian Hall of the University of Edinburgh for their paper “Novel update techniques for the revised s...

Naddef [3] shows that the Hirsch conjecture is true for (0,1)-polytopes by proving that the diameter of any (0, 1)-polytope in d-dimensional Euclidean space is at most d. In this short paper, we give a simple proof for the diameter. The proof is based on the number of solutions generated by the simplex method for a linear programming problem. Our work is motivated by Kitahara and Mizuno [2], in...

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...

This paper presents an original approach for recognizing human activities in video sequences. A human activity is seen as a temporal sequence of elementary action probabilities. Actions are first generically learned using a robust action recognition method based on optical flow estimation and a cross-dataset training process. Activities are then projected as trajectories on the semantic simplex...

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 ...

We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) Yang–Baxter (2-simplex), respectively. examine general structure (2n + 1)-gon 2n-simplex equations in direct sums vector spaces. Then, we provide a construction for their solutions, parameterized by elements Grassmannian Gr(n 1, 2n 1).

We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bound...