A continuous approach to nonlinear integer programming

摘要

This paper is concerned with nonlinear integer programming problems— unconstrained and constrained as well as mixed. The problems are transformed into nonlinear global optimization problems and then solved by the filled function transformation method. This approach should be efficient, since it has been shown that the filled function transformation method is efficient in solving global optimization problems with large numbers (up to 3025 in the present examples) of local minimizers. However, the sense of “efficient” as “having polynomial complexity in the worst or average case” is not suitable for nonlinear integer programming problems, since the complexity of a nonlinear programming algorithm is in general nonpolynomial.