1. Linear Programming Problems 1.1. Formulation of Linear Programming Problems 1.2. Examples 1.3. Different Forms of Programs and Transformations 2. Primal and Dual Programs and Polyhedra 2.1 Duality 2.2. Linear Inequalities and Polyhedra 3. The Simplex Method 3.1. The Restriction-oriented Simplex Method 3.2. The Variable-oriented Simplex Method 3.3. Modifications of Methods and Problems 3.4. T...

The dual simplex method is frequently the most efficient technique for solving linear programming (LP) problems. This thesis describes an efficient implementation of the sequential dual simplex method and the design and development of two parallel dual simplex solvers. In serial, many advanced techniques for the (dual) simplex method are implemented, including sparse LU factorization, hyper-spa...

L1 norm estimator has been widely used as a robust parameter estimation method for outlier detection. Different algorithms have been applied for L1 norm minimization among which the linear programming problem based on the simplex method is well known. In the present contribution, in order to solve an L1 norm minimization problem in a linear model, an interior point algorithm is developed which ...

In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multi-variable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a...

We will derive two results of the primal simplex method by constructing simple LP instances on 0-1 polytopes. First, for any 0-1 polytope and any of its two vertices, we can construct an LP instance for which the simplex method finds a path between them, whose length is at most the dimension of the polytope. This proves a well-known result that the diameter of any 0-1 polytope is bounded by its...

The indirect immunoperoxidase method was applied to the rapid diagnosis of mucocutaneous herpes simplex virus infection. Specimens were obtained directly from lesions at various stages in their evolution. The immunoperoxidase method identified herpes simplex virus-infected cells in 91% of vesicular lesions which were positive by standard virological culture. At later stages, the number of cases...

The simplex method is frequently the most efficient method of solving linear programming (LP) problems. This paper reviews previous attempts to parallelise the simplex method in relation to efficient serial simplex techniques and the nature of practical LP problems. For the major challenge of solving general large sparse LP problems, there has been no parallelisation of the simplex method that ...

Based on the syllogism of formal logic and triangulation theory of algebraic topology, a new method of knowledge representation with 2-simplex called simplex representation is given in this paper. To show differences, the method is compared with others. The simplex representation has special characteristics in representation abilities, expression ability, and representation modality. General Te...

Generalizations of the well-known simplex method for linear programming are available to solve the piecewise linear programming problem and the linear fractional programming problem. In this paper we consider a further generalization of the simplex method to solve piecewise linear fractional programming problems unifying the simplex method for linear programs, piecewise linear programs, and the...

In this paper, a novel fuzzy simplex sliding-mode controller is proposed for controlling a multivariable nonlinear system. The fuzzy logic control (FLC) algorithm and simplex sliding-mode control (SSMC) theory are integrated to form the fuzzy simplex sliding mode control (FSSMC) scheme which improves the system states response and reduces system states chattering phenomenon. In this paper, at f...