Linear-fractional programming: Difference between revisions

Revision as of 21:32, 10 October 2010

Revision as of 13:43, 3 December 2010

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For example, if in the frame of LP we maximize '''profit = income − cost''' and obtain maximal profit of 100 units (= $1100 of income − 1000$ of cost), then using LFP we can obtain only $10 of profit which requires only $50 of investment. Thus, in LP we have efficiency $100/$1000 = 0.1, at the same time LFP provides efficiency equal to $10/$50 = 0.2.

Fractional-linear programs are [[quasiconvex function|quasiconvex]] [[convex minimization|minimization]] problems with a [[monotonicity|monotone]] property, "pseudoconvexity" which is a stronger property than [[quasiconvex function|quasiconvexity]]. A fractional-linear objective function has both "pseudoconvexity" and "pseudoconcavity", these properties allowing FLP problems to be solved by a variant of the [[simplex algorithm]] (of [[George B. Dantzig]]).<ref>
Chapter five: {{cite book| last=Craven|first=B. D.|title=Fractional programming|series=Sigma Series in Applied Mathematics|volume=4|publisher=Heldermann Verlag|___location=Berlin|year=1988|pages=145|isbn=3-88538-404-3 |id={{MR|949209}}| }}</ref><ref> {{cite article | last1=Kruk | first1=Serge|last2=Wolkowicz|first2=Henry|title=Pseudolinear programming | url=http://www.jstor.org/stable/2653207 |journal=[[SIAM Review]]|volume=41 |year=1999 |number=4 |pages=795-805 |id={{MR|1723002}}.{{jstor|2653207}}.{{doi|DOI:10.1137/S0036144598335259}}| }}

</ref><ref> {{cite article | last1=Mathis|first1=Frank H.|last2=Mathis|first2=Lenora Jane|title=A nonlinear programming algorithm for hospital management |url=http://www.jstor.org/stable/2132826|journal=[[SIAM Review]]|volume=37 |year=1995 |number=2 |pages=230-234|id={{MR|1343214}}.{{jstor|2132826}}.{{doi|DOI:10.1137/1037046}}|}}

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