An Iterative Method for Finding Approximate Feasible Points

It is of interest in various contexts to find approximate feasible points to problems that have equality, inequality and bound constraints. For example, in exhaustive search algorithms for global optimization, it is of interest to construct bounds around approximate feasible points, within which a true feasible point is proven to exist. In such exhaustive search algorithms, the approximate feasible point procedure can repeat a large number of times. So, it’s of interest to have a good algorithm that can compute approximate feasible points quickly. Random search has been suggested. But we will show with both theoretical analysis and test results that more is needed. We have developed and tested a technique of computing approximate feasible points, which combines random search with a generalized Newton