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Báo cáo sinh học: " Research Article Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 931590 6 pages doi 10.1155 2010 931590 Research Article Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions J. Zhang1 and X. X. Huang2 1 School of Mathematics and Physics Chongqing University of Posts and Telecommunications Chongqing 400065 China 2 School of Economics and Business Administration Chongqing University Chongqing 400030 China Correspondence should be addressed to X. X. Huang huangxuexiang@cqu.edu.cn Received 5 February 2010 Revised 23 June 2010 Accepted 30 June 2010 Academic Editor Kok Teo Copyright 2010 J. Zhang and X. X. Huang. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature. 1. Introduction It is known that Lagrangian duality theory is an important issue in optimization theory and methodology What is of special interest in Lagrangian duality theory is the so-called strong duality property that is there exists no duality gap between the primal problem and its Lagrangian dual problem. More specifically the optimal value of the primal problem is equal to that of its Lagrangian dual problem. For a constrained convex program a number of conditions have been obtained for its strong duality property see for example 1-3 and the references therein. It is also well known that penalty method is a very popular method in constrained nonlinear programming 4 . In 5 a quadratic penalization technique was applied to establish strong Lagrangian duality property for an invex program under the assumption that the objective function is coercive. In this paper we will .