广义次微分及其应用.pdf

第 8 卷　第 1期 　　　　　　　　　运　筹　与　管　理　 　 　 　 　 　 　 　Vol. 8, No. 1 1999 年3 月　 　 　OPERATIONS RESEARCH AND MANAGEMENT SCIENCE 　 　 　 Mar . , 1999 欧宜贵 ( , , , 570228) , , ; ; ; O221 Generlized Subdifferent ial and it s Applications Ou Yigui (H ainan Univ er si ty , H aiK ou, H ainan , 570228 Ch ina) AbstractIn this paper , I present the strong optimality conditions for a class of functions y means of the generalized su differential. Moreover, I give its applications to the sta ility the- ory and minimization. Key wordsgeneralized su differential; sta ility ; minimization 0 [ 1] - n : x f :R R , f (x ) ~ ( ) , ( ) [ 2] f x f x [ 1, 2, 3] , , , 1 : minf (x ) (P ) x R n n * : , = ( ) f R R X Arg minf x x R n : 1998- 11- 18 , , 1965 2 , , 60 运　筹　与　管　理　　　　　　　1999 年第8 卷 [ 4] f , d : 5f (x ) = {g Rn :g T (y - x ) f (y ) - f (x ) , P y Rn } f ø(x ; d) = lim[f (x + td ) - f (x ) ] / t t 0 T * * n * f ø(x ; d ) = max (g d ) , X = {x R : 0 5f (x ) } g 5f (x ) , , * * 1. 1 0, ( ) ( ) + , ( ) -