Statement of the Main Problem. Basic Result

Stefan M. Stefanov ()
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Stefan M. Stefanov: South-West University Neofit Rilski

Chapter Chapter 5 in Separable Optimization, 2021, pp 133-139 from Springer

Abstract: Abstract Consider the following convex separable programming problem (C): $$\begin{aligned} \min \> \bigg \{c(\mathbf{x}) = \sum _{j \in J } \> c_j (x_j)\bigg \} \end{aligned}$$ min { c ( x ) = ∑ j ∈ J c j ( x j ) } subject to $$\begin{aligned} \sum _{j \in J} d_j (x_j) \le \alpha \end{aligned}$$ ∑ j ∈ J d j ( x j ) ≤ α $$\begin{aligned} a_j \le x_j \le b_j , \quad j \in J, \end{aligned}$$ a j ≤ x j ≤ b j , j ∈ J , where $$c_j(x_j)$$ c j ( x j ) and $$d_j(x_j)$$ d j ( x j ) are twice differentiable convexSeparable programmingconvex with bounded variables functions, defined on the open convex sets $$X_j$$ X j in $${\mathrm{I\!R}}$$ I R , $$j \in J$$ j ∈ J , respectively; $$d_j'(x_j) > 0$$ d j ′ ( x j ) > 0 for every $$ j\in J, \> \mathbf{x} = (x_j)_{j \in J}$$ j ∈ J , x = ( x j ) j ∈ J , and $$J {\mathop {=}\limits ^\mathrm{def}} \{1,...,n\}$$ J = def { 1 , . . . , n } .

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-78401-0_5

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DOI: 10.1007/978-3-030-78401-0_5

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