(!****************************************************** Mosel Example Problems ====================== file approx.mos ``````````````` Function approximation with SOS2 (c) 2008 Fair Isaac Corporation author: S. Heipcke, Sep. 2006 *******************************************************!) model "Approximation" uses "mmxprs" declarations NB = 5 BREAKS = 1..NB R,F: array(BREAKS) of real ! Coordinates of break points x,f: mpvar ! Decision variables y: array(BREAKS) of mpvar ! Weight variables end-declarations R:: [1, 2.2, 3.4, 4.8, 6,5] F:: [2, 3.2, 1.4, 2.5, 0,8] RefRow:= sum(i in BREAKS) R(i)*y(i) x = RefRow f = sum(i in BREAKS) F(i)*y(i) ! Convexity constraint sum(i in BREAKS) y(i) = 1 ! SOS2 definition RefRow is_sos2 ! Alternative SOS definition (to be used for 0-valued RefRow coefficients): ! makesos2(union(i in BREAKS) {y(i)}, RefRow) (! Alternative formulation using binaries instead of SOS2: declarations b: array(1..NB-1) of mpvar end-declarations sum(i in 1..NB-1) b(i) = 1 forall(i in 1..NB-1) b(i) is_binary forall(i in BREAKS) y(i) <= if(i>1, b(i-1), 0) + if(i<NB, b(i), 0) !) ! Bounds 1<=x; x<=6,5 ! Solve the problem minimize(f) writeln("Objective value: ", getobjval) writeln("x: ", getsol(x)) end-model