关于非线性规划的逆对偶性

On Converse Duality in Nonlinear Programming

对带锥约束的非线性规划问题,Nanda和Das在1996年引入了四类对偶模型并给出了相应的各种对偶定理[1]。2000年,Chandra和Abha指出Nanda和Das的文章有错误,通过修正,他们提出了四类新对偶模型。在广义伪凸性条件下,Chandra和Abha获得了新对偶模型的弱对偶性和强对偶性结果[2]。本文建立了四类Chandra Abha对偶模型的逆对偶定理,同时也指出了Nanda和Das文章中有关逆对偶性结果证明的不正确性。

For nonlinear programming with cone constraints,Nanda and Das (1996) introduced four dual models and discussed their various duality theorems (see,European Journal of Operational Research 88(1996) 572-577).However,Chandra and Abha in 2000 pointed out that there were some deficiencies in the work by Nanda and Das.They further suggested appropriate modifications for the study of weak and strong dualities under pesudo-invexity assumptions (see,European Journal of Operational Research 122(2000)161-165).We observe that no consideration in Chandra and Das′s paper on converse duality results for modified dual models,and that the proofs of converse duality theorems in Nanda and Das′s paper are not totally correct.In this paper,we use the Fritz John Theorem to establish several converse duality results for four kinds of Chandra-Abha dual models and point out some mistakes in the proof for converse duality results of Nanda and Das′s paper.