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January  2011, 7(1): 67-78. doi: 10.3934/jimo.2011.7.67

## Global optimality conditions for some classes of polynomial integer programming problems

 1 Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China, China 2 School of Information Technology and Mathematical Sciences, University of Ballarat, Victoria 3353

Received  November 2008 Revised  September 2010 Published  January 2011

In this paper, some verifiable necessary global optimality conditions and sufficient global optimality conditions for some classes of polynomial integer programming problems are established. The relationships between these necessary global optimality conditions and these sufficient global optimality conditions are also discussed. The main theoretical tool for establishing these optimality conditions is abstract convexity.
Citation: Jing Quan, Zhiyou Wu, Guoquan Li. Global optimality conditions for some classes of polynomial integer programming problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 67-78. doi: 10.3934/jimo.2011.7.67
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