Search direction improvement for gradient-based optimization problems

摘要

Most gradient-based optimization algorithms calculate the search vector using the gradient or the Hessian of the objective function. This causes the optimization algorithm to perform poorly in cases where the dimensionality of the objective function is less than that of the problem. Though some methods like the Modified Method of Feasible Directions tend to overcome this shortcoming, they again perform poorly in situations of competing constraints. This paper introduces a simple modification in the calculation of the search vector that not only provides significant improvements in the solutions of optimization problems but also helps to reduce or, in some cases, overcome the problem of competing constraints.