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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{c T x;Ax=0,e T x=1,x0} the author considers a program with entropic barrier function (P μ ) min{c T x+μ j x j logx j ;Ax=0,e T x=1,x0} and shows by using a geometric programming technique that the dual problem (D μ ) to (P μ ) is an unconstrained convex programming problem. Explicit formulae are derived for the computation of ε- optimal solutions to (P) and to its dual (D) from the optimal solution to (D μ ). Solving (D μ ) via unconstrained minimization techniques is discussed briefly.
Reviewer: J.Rohn (Praha)

MSC:
90C05Linear programming
90C25Convex programming
90-08Computational methods (optimization)
90C30Nonlinear programming
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