Geodesic
Solving the linear complementarity problem through concave programming
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 602-608

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The following complementarity problem is considered: to find $x\in R^n$, $y\in R^n$, satisfying the conditions $x\ge0$, $y\ge0$, $y=Ax-b$, $(x,y)=0$. A problem of linear programming is reducible to this statement, but not vice versa. The complementarity problem is shown to be reducible to a problem of concave programming with linear constraints and a piecewise linear target function. 
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     title = {Solving the linear complementarity problem through concave programming},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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Nguyen Van Thoai; Hoang Tuy. Solving the linear complementarity problem through concave programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 3, pp. 602-608. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_3_a8/