We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal valu...

In this work, we propose a two-stage approach to strengthen piecewise McCormick relaxations for mixed-integer nonlinear programs (MINLP) with multi-linear terms. In the first stage, we exploit Constraint Programing (CP) techniques to contract the variable bounds. In the second stage we partition the variables domains using a dynamic multivariate partitioning scheme. Instead of equally partition...

To solve the problem of energy saving in the design of wireless sensor networks, a new maximum lifetime routing algorithm was proposed based on uneven cluster, linear programing and fuzzy set theory (UCLF) in wireless sensor networks, which formulated the system maximum lifetime problem as a linear programming problem and selected cluster head based on fuzzy set theory, where the objectives is ...

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...

Sylvester's identity is a well-known identity which can be used to prove that certain Gaussian elimination algorithms are fraction-free. In this paper we will generalize Sylvester's identity and use it to prove that certain random Gaussian elimination algorithms are fraction-free. This can be used to yield fraction-free algorithms for solving Ax = b (x 0) and for the simplex method in linear pr...

In the rst part of the paper we survey some far-reaching applications of the basic facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concerning the simplex algorithm. We describe subexponential randomized pivot rules and upper bounds on the diameter of graphs of polytopes.

When solving families of related linear programming (LP) problems and many classes of single LP problems, the simplex method is the preferred computational technique. Hitherto there has been no efficient parallel implementation of the simplex method that gives good speed-up on general, large sparse LP problems. This paper presents a variant of the dual simplex method and a prototype parallelisa...

Using a model-based optimization, a neural network model is used to compute the optimal values of gas injection rate and oil rate of a gas lift production system. Two cases are analyzed: a) A single well production system and b) A production system composed by two gas lifted wells. For both cases minimizing the objective function of the proposed strategy shows the ability of the neural networks...

In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal matchings, we introduce matchingcover pairs to efficiently handle maximality in the local structure, and develop a polynomial time algorithm. For path matchings, w...