斜向扰动的下可微稳定性<sup>*</sup>

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斜向扰动的下可微稳定性^*

基金项目: * 国家自然科学基金资助项目

摘要: Laurent和Rockafellar研究了凸极小化问题中的扰动和稳定性问题.Laurent分别就水平扰动和垂直扰动讨论了下可微稳定性条件.本文推广了Laurent的若干结果.给出了某些斜向扰动的下可微稳定性条件.

Abstract: Lanrem and Rockafellar have studied certain problems of perturbation and of stability in convex minimization problems.Laurent has discussed inf-dif-stability conditions respectively for horizontal perturbation and for vertical perturbation.In this paper, we generalize some results of Laurent^[1] by giving several inf-dif-slability conditions of oblique perturbation.

[1]	Laurent,P.J.,Approximation at Optimisation,Hermann(1972).
[2]	Joly,J.L.and P.J.Laurent.,Stability and duality in convex minimization problems,M.R.C.Techn.Report 1090,Univ.of Wisc.(1970) ;RIRO.,(1971),3-42.
[3]	Rockafellar.R.T.,Convex Analysis,Prinston Univ.Press(1970).
[4]	Chen Song-qiang(陈嵩强),Un theoreme de stabilite des perturbation oblique dans Le problème de minimisation comvexe,Acta Mathematica Scientia,4,2(1984),243-258.