This article is cited in 1 paper

Penalty, barrier, quasi-barrier functions and functions inverse to them

A. G. Birjukov, A. V. Chernov, Yu. G. Chernova, Yu. I. Sharovatova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The methods of external penalty functions, internal penalty functions and quasi-barrier functions for solving problems of mathematical programming are considered. New quasi-barrier functions are proposed. The theorems of convergence of the indicated methods to the solution of mathematical programming problems are proved. The properties of these functions are considered for their transformations: differentiation, integration, construction of functions inverse to them.

Keywords: external penalty functions, internal penalty functions, barrier penalty functions, inverse functions, quasi-barrier functions, mathematical programming problem, differential barriers, power differential barriers, entropy differential barriers, convergence of differential barriers methods to solving mathematical programming problems.