[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

[maths] Lagrange Multipliers - Optimal operation of power systems

Hi ca'c ba'c Iga Nguyen, Hoang Duong Tuan and others,

Ca'ch dday ho+n 2 tha'ng to^i co' ye^u ca^`u VNSA giu'p ddo+~ ve^` (strong
or heuristic) bounds  cu?a ca'c he^. so^' Lagrange trong viec giai bai toan
toi uu (van hanh he thong dien) bang phuong phap Lagrangian Relaxation.

Toi xin ca?m on chi Iga Nguyen da goi y ve viec dua bai toan ve spectrum
(eigenvalues). Tuy nhien, viec nay ngoai kha nang va background cua toi :).
Goi y cua anh Hoang Duong Tuan xem ra thuc te hon ca. Toi da doc mot so
chuong trong quyen sa'ch "Nonlinear programming" (Bertsekas, 1995). Quyen
sa'ch viet hay, su pham voi nhieu minh hoa (binh dan hon sa'ch cua David
Luenberger), tuy nhien van khong co cho nao cho ta mot kha'i niem ro rang ve
viec ti`m bounds. Co' le~ la do quan niem du`ng cac LM nhu auxiliary
variables de giai primal problem.

Du` day chi la mot trong research directions, toi van "tra(n tro+?" ve^` van
de nay vi cho rang day la mot standard problem voi da^n toa'n. Tua^`n truoc,
toi ti`m duoc mot database rat tot ve toan - MathScinet va tra thu+? thi`
tim duoc mot so references ddu'ng nhu+ to^i ca^`n. Xin ghi lai de cac ba'c
nao co quan tam co the tien tham khao:

1. Gauvin, J, 1977, "A necessary and sufficient regularity condition to have
bounded multipliers in nonconvex programming", Mathematical Programming
(12), pp.136-138
2. Mangasarian, O.L, 1985, "Computable numerical bounds for Lagrange
multipliers of stationary points of nonconvex differentiable non-linear
programs", Operations research letters, vol 4, no 2, pp. 47-48
3. Hansen, E.R and Walster, G.W, 1993, "Bounds for Lagrange Multipliers and
optimal points", Computers Math. Applications, vol 25, no 10/11, pp.59-69

Mot insightful reference kha'c (tuy khong noi ro ve bounds) cua mot "la~o
la`ng":
4. Rockafellar, R.T, 1993, "Lagrangian Multipliers and optimality", SIAM
review, vol.35, no.2, pp.183-238
Voi ca'c references nay, ve mat ly thuyet, van de cua toi da sang to? duoi
mot so dieu kien va gia thiet cu the.

Lan nua, xin cam on chi. Iga Nguyen va anh Hoang Duong Tuan dda~ nhiet tinh
giup ddo+~.
Cheers,
+-----------------------------------------------------------------+
  Thai Doan Hoang Cau
  Electrical energy systems laboratory, UNSW
  Home addr.: 16/22 Kennedy st, Kingsford,
                       NSW 2032, Sydney, Australia
  Tel: 9399 6653 (home), 9385 4061 (work)
+-----------------------------------------------------------------+