TY - JOUR
T1 - Necessary and sufficient condition on decomposable convex programming
AU - Chu, Liang Ju
PY - 1996/7
Y1 - 1996/7
N2 - This paper considers a kind of decomposible convex programming: (P) min{f(x); xε C}, and its corresponding decomposible variational inequality DVI(f, C), where f(x):=f1(x1)+f2 (x2)+···+fn(xn), for every x:=(x1, x2, ···, xn) and C:=C1xC2x···xCn···xCn . Under the constraint qualification 0 ε ri(piin = 1 (coD (∂fi) - Ci),we show that x is a solution to DVI(f, C) if, and only if, x is an optimal solution of (P).
AB - This paper considers a kind of decomposible convex programming: (P) min{f(x); xε C}, and its corresponding decomposible variational inequality DVI(f, C), where f(x):=f1(x1)+f2 (x2)+···+fn(xn), for every x:=(x1, x2, ···, xn) and C:=C1xC2x···xCn···xCn . Under the constraint qualification 0 ε ri(piin = 1 (coD (∂fi) - Ci),we show that x is a solution to DVI(f, C) if, and only if, x is an optimal solution of (P).
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M3 - Article
AN - SCOPUS:0030191167
SN - 0255-6588
VL - 20
SP - 351
EP - 359
JO - Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering
JF - Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering
IS - 4
ER -