Global optimality conditions for some classes of polynomial integer programming problems

Jing Quan; Zhiyou Wu; Guoquan Li

doi:10.3934/jimo.2011.7.67

Article Contents

2011, Volume 7, Issue 1: 67-78. Doi: 10.3934/jimo.2011.7.67

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Global optimality conditions for some classes of polynomial integer programming problems

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

Received: November 2008

Revised: September 2010

Published: January 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C10, 90C46, 90C26; Secondary: 26C05.

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