k f (sk)=opt( vk(Sk,uk)f(sk+d) n+1(n+1 k+1 2 k f(Skd=optv (skil,un) X(sk) f(s)=11 2  k s1 u1 s2 u2 s3 sk uk sk+1 1 2  k s1 u1 s2 u2 s3 sk uk sk+1 ( ) { ( , ) ( )} 1 k k 1 k k 1 k u k k f s opt v s u f s k + = + + − ( ) 0 f 0 s1 = ( ) { ( , ) ( )} = k k k + k+1 k+1 u k k f s opt v s u f s k f n+1 (sn+1 ) = 0 × × 1 1