Necessary and sufficient condition on decomposable convex programming

Liang Ju Chu

Necessary and sufficient condition on decomposable convex programming

Liang Ju Chu^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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)+···+f_n(x_n), for every x:=(x₁, x₂, ···, x_n) and C:=C₁xC₂x···xC_n···xC_n . Under the constraint qualification 0 ε ri(pi_iⁿ = 1 (coD (∂f_i) - C_i),we show that x is a solution to DVI(f, C) if, and only if, x is an optimal solution of (P).

Original language	English
Pages (from-to)	351-359
Number of pages	9
Journal	Proceedings of the National Science Council, Republic of China, Part A: Physical Science and Engineering
Volume	20
Issue number	4
Publication status	Published - 1996 Jul

ASJC Scopus subject areas

General Engineering

Cite this

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abstract = "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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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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SN - 0255-6588

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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

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Necessary and sufficient condition on decomposable convex programming

Abstract

ASJC Scopus subject areas

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