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A nonlinear equation for linear programming (1986)

Smith, P. W. ; Wolkowicz, H.

Springer

Mathematical programming 34 (1986), S. 235-238

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ISSN: 1436-4646

Keywords: Linear Programming ; Characterization of Optimality ; Dual Program

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01580588

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