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An unconstrained convex programming view of linear programming. (English) Zbl 0759.90064
For a linear program in Karmarkar standard form (P) $min\left\{{c}^{T}x;Ax=0,{e}^{T}x=1,x\ge 0\right\}$ the author considers a program with entropic barrier function $\left({\text{P}}_{\mu }\right)$ $min\left\{{c}^{T}x+\mu {\sum }_{j}{x}_{j}log{x}_{j};Ax=0,{e}^{T}x=1,x\ge 0\right\}$ and shows by using a geometric programming technique that the dual problem $\left({\text{D}}_{\mu }\right)$ to $\left({\text{P}}_{\mu }\right)$ is an unconstrained convex programming problem. Explicit formulae are derived for the computation of $\epsilon$- optimal solutions to (P) and to its dual (D) from the optimal solution to $\left({\text{D}}_{\mu }\right)$. Solving $\left({\text{D}}_{\mu }\right)$ via unconstrained minimization techniques is discussed briefly.
Reviewer: J.Rohn (Praha)

##### MSC:
 90C05 Linear programming 90C25 Convex programming 90-08 Computational methods (optimization) 90C30 Nonlinear programming
##### References:
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