Methods of embedding-cutting off in problems of mathematical programming
The author considers general iterative embedding procedures for finding a global minimizer of a continuous real-valued function on a compact subset of the \(n\)-dimensional Euclidean space. In particular a cutting type procedure is studied for inequality constrained problems for which the variables stay in a compact set and the objective function and the constraint functions have concave minorants. The latter is particularly true when the functions are linear, convex, or concave. As an example of the procedure a specific cutting plane method is investigated which is suitable for the solution of small-dimensional problems with linear inequality constraints and lower and upper bounds on the variables. Particular attention is devoted to the case that the objective function of the problem is concave. The cutting plane method is tested on some randomly generated quadratic functions with an indefinite matrix and up to 10 variables.
scientific article; zbMATH DE number 5796470