Application of Interval Slopes in Nonsmooth One-Dimensional Optimization Problems

The interval interpretation of a first-order divided difference, namely, interval slope is considered. Some properties of interval slopes, including ones for convex (concave) functions are proved. Based on the interval slope, necessary and sufficient conditions for the monotonicity of a function are formulated and proved. These criteria are used to propose an algorithm for the global optimization of a one-variable function taking into account its monotonicity. Numerical experiments are conducted that show that the developed global optimization method is applicable in the nondifferentiable case and significantly accelerates finding an approximate global optimum as compared with the basic ve-rsion.