It has been recently claimed that the most-obtuse-angle pivot rule is one of the best choices for Phase I linear programs based on the simplex method. In this short note we give two instances of Phase I cycling under such ratio-test-free rule, both when it is used to obtain primal feasibility and when trying to achieve dual feasibility with its unnormalized counterpart. A crash procedure that i...

The trace map has been used very successfully to generate cocyclic complex and Butson Hadamard matrices and simplex codes over Z4 and Z2s . We extend this technique to obtain new linear codes over Zps . It is worth nothing here that these codes are cocyclic but not simplex codes. Further we find that the construction method also gives Butson Hadamard matrices of order p.

This paper studies senary simplex codes of type α and two punctured versions of these codes (type β and γ). Self-orthogonality, torsion codes, weight distribution and weight hierarchy properties are studied. We give a new construction of senary codes via their binary and ternary counterparts, and show that type α and β simplex codes can be constructed by this method.

It has been a challenge for mathematicians to theoretically confirm the extremely good performance of simplex algorithms for linear programming. We have confirmed that a certain variant of the simplex method solves problems of order m X n in an expected number of steps which is bounded between two quadratic functions of the smaller dimension of the problem. Our probabilistic assumptions are rat...

We prove that the simplex method with the highest gain/most-negative-reduced cost pivoting rule converges in strongly polynomial time for deterministic Markov decision processes (MDPs) regardless of the discount factor. For a deterministic MDP with n states and m actions, we prove the simplex method runs in O(nm log n) iterations if the discount factor is uniform and O(nm log n) iterations if e...

The objective of this work is to develop more efficient alternatives for Simplex method implementation. Techniques of the Simplex basis LU factorization update are developed to improve the solution of the Simplex method linear systems to achieve a column static reordering of the matrix. A simulation of the Simplex method is implemented, with the change of basis obtained from MINOS. Only the fac...

We propose in this paper a simple but efficient modification of the well-known Nelder-Mead (NM) simplex search method for unconstrained optimization. Instead of moving all n simplex vertices at once in the direction of the best vertex, our ”shrink” step moves them in the same direction but one by one until an improvement is obtained. In addition, for solving non-convex problems, we simply resta...

The pupose of this paper is modeling of Partial Digest Problem (PDP) as a mathematical programming problem. In this paper we present a new viewpoint of PDP. We formulate the PDP as a continuous optimization problem and develope a method to solve this problem. Finally we constract a linear programming model for the problem with an additional constraint. This later model can be solved by the simp...

background: human pathogens that can cause infertility may also affect sperm count and quality. viral infections can be considered as direct and/or indirect cause of male factor infertility. objective: our goal was to investigate the prevalence of herpes simplex virus in the semen of infertile men attending the avicenna infertility clinic, and to compare it with the herpes virus serology result...

Although the Simplex Method (SM) developed for Dantzig is efficient for solving many linear programming problems (LPs), there are constructions of hard linear programs as the Klee-Minty cubes and another deformed products, where this method has an exponential behavior. This work presents the integration of genetic algorithms (GA) and SM to fastly reach the optimum of this type of problems. This...