Global optimality conditions and optimization methods for quadratic integer programming problems
This paper establishes some sufficient and some necessary global optimality conditions for quadratic integer programming problems. The results given in this work extend results presented in [\textit{A. Beck} and \textit{M. Teboulle}, SIAM J. Optim. 11, No. 1, 179--188 (2000; Zbl 0990.90089)]; [\textit{W. Chen} and \textit{L. Zhang}, J. Glob. Optim. 46, No. 2, 191--206 (2010; Zbl 1209.90292)] and [\textit{V. Jeyakumar}, \textit{A. M. Rubinov} and \textit{Z.Y. Wu}, Math. Program. 110, No. 3, 521--541 (2007; Zbl 1206.90178)]. The authors develop a new local optimization method by exploiting the obtained necessary global optimality condition and propose a new global optimization method by combining the sufficient global optimality condition, the local optimization method and an auxiliary function. Some numerical examples are provided to illustrate the performance of both optimization methods.
scientific article; zbMATH DE number 5988576
scientific article