Global optimization with data perturbations (Q1086171)

In previous publications algorithms by the author were described for solving the global nonlinear optimization problem for the unconstrained and the inequality constrained cases. The algorithms are applicable when the objective function is twice continuously differentiable and the constraints are continuously differentiable. They provide infallible bounds on the minimal value of the objective function and the point(s) at which it occurs. In this paper, we show these algorithms are equally applicable when the data is either exact or perturbed. In the latter case, it is assumed that perturbations can be described by specifying the coefficients in the objective and constraint functions as intervals. No changes in the programs are required to solve the perturbed case. Only the objective and constraint functions change to reflect the uncertainty in data. Numerical results are given.