Second-order necessary and sufficient optimality conditions for optimization problems and applications to control theory. (English)
SIAM J. Optim. 13, No.2, 406-431 (2002)
Neu ko tim duoc thi de lai dia chi email to se gui cho. Bai bao nay viet cho truong hop tong quat nhung co dua ra 1 VD cho ODE. Nho no ban co the xac dinh duoc optimality condition (va tinh dao ham x theo u).
Thu 2 la ham muc tieu va dieu kien cho x(T). Khong hieu de bai ra la the hay day la bai toan ban tu dat ra de giai 1 van de thuc te? Lieu ta co the viet ham muc tieu duoi dang
voi K>0 du lon duoc ko? Nhu vay ta da buoc x1(T)=L va x2(T)=0 va ban co the quen di dieu kien bien tai T va xet bai toan ODE voi gia tri ban dau x(0)=0. Tuy nhien u1 co thuc su la min hay ko thi chiu. Van de o cho neu K nho thi dieu kien bien tai T ko duoc thoa man (xap xi chua du tot), con neu K lon thi u1^4 dt lai tro nen qua nho so voi J, va nhu vay ko the kiem soat duoc hoan toan do lon cua u1. Neu va^~n de^? bai toan duoi dang cu thi to khong biet giai the nao. Ma tai sao phai can u1^4 vay? To khoai ham bac 2 hon, do phuc tap.
Ma ban dinh dung gi de giai ODE va thuat toan nao de toi uu vay?