Abstract
We present a characterization of the ‘normal’ optimal solution of the linear program given in canonical form max{c tx: Ax = b, x ≥ 0}. (P) We show thatx * is the optimal solution of (P), of minimal norm, if and only if there exists anR > 0 such that, for eachr ≥ R, we havex * = (rc − Atλr)+. Thus, we can findx * by solving the following equation forλ r A(rc − Atλr)+ = b. Moreover,(1/r)λ r then ‘converges’ to a solution of the dual program.
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On leave from The University of Alberta, Edmonton, Canada. Research partially supported by the National Science and Engineering Research Council of Canada.
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Smith, P.W., Wolkowicz, H. A nonlinear equation for linear programming. Mathematical Programming 34, 235–238 (1986). https://doi.org/10.1007/BF01580588
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DOI: https://doi.org/10.1007/BF01580588