A basis-deficiency-allowing primal phase-I algorithm using the most-obtuse-angle column rule

Abstract

The dual Phase-I algorithm using the most-obtuse-angle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basis-deficiency-allowing context. In this paper, we establish a basis-deficiency-allowing Phase-I algorithm using the so-called most-obtuseangle column pivot rule to produce a primal (deficient or full) basis. Our computational experiments with the smallest test problems from the standard NETLIB set show that a dense projected-gradient implementation largely outperforms that of the variation of the primal simplex method from the commercial code MATLAB LINPROG vl.17, and that a sparse projected-gradient implementation of a normalized revised version of the proposed algorithm runs 34°~ faster than the sparse implementation of the primal simplex method included in the commercial code TOMLAB LPSOLVE V3.0. (~)

Management of Production Processes in a Heating Company

“…Gurobi [15] is a commercial software for solving large-scale linear programming and mixed-integer problems. It is known for its ability to use multi-core processors efficiently, thus achieving high computing power com-pared to the LpSolve tool [16]. Mathematical modelling has an essential role in quantifying and comparing the effects and various factors, constraints or objectives on the performance of a system or process.…”

A non-monotonic infleasible interior-exterior point algorithm for linear programming

“…These algorithms have the advantage that they can be initialized at arbitrary starting solutions and present a great degree of flexibility in designing particular algorithmic variants. Li et al [68] proposed a primal Phase I method using the most -obtuse -angle column pivoting rule. Another approach for solving LPs has been proposed by Jurik [54].…”