The approximation algorithm for solving a sort of non-smooth programming
The authors present an approximation algorithm for solving a sort of non-smooth programming, in which the objective function is the Hölder function and the feasible region is contained in a rectangle (viz. hyper-rectangle). To establish the algorithm, the properties of the Hölder function and an approximation of the function by using Bernstein \(\alpha\)-polynomials are studied. The convergence of the algorithm can be guaranteed by the exhaustive of the bisection of the rectangle. The feasibility of the algorithm is validated by solving an example.
scientific article; zbMATH DE number 5162006