Inclusion functions and global optimization II

Applied Interval Analysis

“…The resulting algorithm does not use any contractor and does not perform any local search. The next two examples (Walster et al, 1985;Moore and Ratschek, 1988;Jansson and Kniippel, 1995) illustrate the efficiency of the Moore-Skelboe algorithm and the influence of the dimension of the problem. …”

A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

“…The inclusion function is not unique and depends on the formal expression of f [28]. This paper uses the natural inclusion functions and builds them by replacing each real variable x i by an interval variable [x i ] and each operator or function by its interval evaluation.…”

A Fuzzy Adaptive Partitioning Algorithm (FAPA) for Global Optimization

“…This prior model of f (x)is integrated with sample information resulting in an adaptive posterior model of f (x) [1,2]. Another interval estimation approach is based on inclusion functions [3][4][5][6] where the bounds on f (x) within a specific interval are calculated by replacing the real operations in f (x) by their pre-determined interval operations resulting in an interval on f (x) for each operation. Then, when all the terms are aggregated, an enclosure of f (x) is obtained.…”