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Simplex algorithm
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==Linear-fractional programming== {{Main|Linear-fractional programming}} [[Linear-fractional programming|Linear–fractional programming]] (LFP) is a generalization of [[linear programming]] (LP). In LP the objective function is a [[linear functional|linear function]], while the objective function of a linear–fractional program is a ratio of two linear functions. In other words, a linear program is a fractional–linear program in which the denominator is the constant function having the value one everywhere. A linear–fractional program can be solved by a variant of the simplex algorithm<ref>{{harvtxt|Murty|1983|loc=Chapter 3.20 (pp. 160–164) and pp. 168 and 179}}</ref><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=978-3-88538-404-5|mr=949209}}</ref><ref>{{cite journal|last1=Kruk|first1=Serge|last2=Wolkowicz|first2=Henry|title=Pseudolinear programming|journal=[[SIAM Review]]|volume=41|year=1999|issue=4|pages=795–805|mr=1723002|jstor=2653207|doi=10.1137/S0036144598335259|citeseerx=10.1.1.53.7355|bibcode=1999SIAMR..41..795K}} </ref><ref>{{cite journal|last1=Mathis|first1=Frank H.|last2=Mathis|first2=Lenora Jane|title=A nonlinear programming algorithm for hospital management|journal=[[SIAM Review]]|volume=37 |year=1995 |issue=2 |pages=230–234|mr=1343214|jstor=2132826|doi=10.1137/1037046|s2cid=120626738 }} </ref> or by the [[criss-cross algorithm]].<ref>{{cite journal|title=The finite criss-cross method for hyperbolic programming|journal=European Journal of Operational Research|volume=114|issue=1| pages=198–214|year=1999|issn=0377-2217|doi=10.1016/S0377-2217(98)00049-6|first1=Tibor|last1=Illés|first2=Ákos|last2=Szirmai|first3=Tamás|last3=Terlaky|url=http://www.cas.mcmaster.ca/~terlaky/files/dut-twi-96-103.ps.gz |citeseerx=10.1.1.36.7090}}</ref>
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