A Perspective on Stochastic Search Efficiency via Quasigradient Techniques in Constrained Models

Abstract

This article examines some of the properties of quasi-Fejer sequences when used in quasi-gradiental techniques as an alternative to stochastic search techniques for optimizing unconstrained mathematical programming models. The convergence and efficiency of the method are analyzed, and its potential use as an interior-point algorithm for optimizing integer linear programming models is explored, ensuring the feasibility of the solution at each stage of the search. To achieve this, it is proposed to remain within the feasible region by using small perturbations around the points found until convergence is reached. This alternative is compared with the traditional Branch and Bound method using software programs available for this purpose. The results obtained suggest that the technique, applied to models with few variables, is inefficient but is practical for large-scale models, since simple changes in the components of the located points generate a feasible sequence that almost always converges.