Comparative Study of Unconstrained Mechanical Optimization Methods Based on Two-variable Rosenbrock Function

Abstract

The unconstrained optimization method (UOM) plays an important role in the field of physics, mathematics, statistics, etc. Rosenbrock function is a 4-degree function with a curved canyon. It is most suitable for testing UOM. However, the test hasn't done. We have written 14 UOM computer programs, 12 of which contain our new algorithm. From the optimal result, the 2-order approximation direction is the best, followed by the conjugate direction, followed by the negative gradient direction. For quadratic fitting function method, linear fitting gradient method and unbounded polyhedron deformation method, a new algorithm for moving points was proposed. When the new point is better than all of the other points, the other points should close up to it. And when the new point is worse than all of the other points, it should close up to the best point or center point. The improvement of moving points makes these optimization directions be effective for complex objective functions.