The prerestorative step in the sequential gradient-restoration algorithm for mathematical programming problems with inequality constraints
Master of Science
The problem of minimizing a function f(x) subject to the constraint r(x) s is considered. Here, f is a scalar, x is an n-vector, and r is a q-vector. The method employed is the sequential gradient-restoration algorithm with complete restoration. In this algorithm, the inequality constraint is transformed into equality constraint by suitable transformations. The sequential gradient-restoration algorithm is composed of the alternate succession of gradient phases and restoration phases. In the gradient phase, one tries to improve the value of the function while avoiding excessive constraint violation. In the restoration phase, one tries to reduce the constraint error, while avoiding excessive change in the value of the function. A modification of the sequential gradlent-restoration algorithm is presented. This modification consists of inserting a prerestorative step prior to any iteration of the algorithm. The result of this modification is to reduce the constraint violating, while leaving unchanged the value of the function. Five numerical examples are given to show the considerable beneficial effects associated with the modification presented here.