Improved techniques for gap-treating and box-splitting in interval Newton Gauss-Seidel steps for global optimization with validation
Ratz, Dietmar · Repository KITopen (Karlsruhe Institute of Technology) · 1996
Interval global optimization algorithms often incorporate an interval Newton Gauss-Seidel step to rapidly reduce the widths of the boxes resulting from the underlying generalized bisection method. It aims at determining the roots of the gradient of the objective function, whereas various other techniques eliminate regions containing roots which do not correspond to global optimizers. The interval Newton Gauss-Seidel step uses extended interval arithmetic which allows the division by intervals containing zero. The latter may produce gaps in the resulting coordinate intervals, which can be used to split the resulting box. We investigate the impact of different gap-treating and box-splitting techniques producing different numbers of subboxes, and we propose strategies which improve the overall efficiency of the interval Newton Gauss-Seidel step and therefore of global optimization methods. We present results of computational experiments with standard global optimization problems.