ramsey.gms:
References:
- Ramsey, F P, A Mathematical Theory of Saving. Economics Journal (1928).
- Murtagh, B A, and Saunders, M A, A Projected Lagrangian Algorithm and its Implementation for Sparse Nonlinear Constraints. Mathematical Programming Study 16 (1982), 84-117.
- Original source: GAMS Model of ramsey.gms from GAMS Model Library
Point:
p1
Best known point: p1 with value -1.4931
<![CDATA[
* NLP written by GAMS Convert at 07/30/01 17:04:25
*
* Equation counts
* Total E G L N X
* 23 22 0 1 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 34 34 0 0 0 0 0 0
* FX 2 2 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 77 55 22 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,objvar;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23;
e1.. 0.759835685651593*x1**0.25 - x12 - x23 =E= 0;
e2.. 0.77686866556676*x2**0.25 - x13 - x24 =E= 0;
e3.. 0.794283468039448*x3**0.25 - x14 - x25 =E= 0;
e4.. 0.812088652256959*x4**0.25 - x15 - x26 =E= 0;
e5.. 0.830292969275008*x5**0.25 - x16 - x27 =E= 0;
e6.. 0.848905366318769*x6**0.25 - x17 - x28 =E= 0;
e7.. 0.867934991180342*x7**0.25 - x18 - x29 =E= 0;
e8.. 0.88739119671479*x8**0.25 - x19 - x30 =E= 0;
e9.. 0.907283545436972*x9**0.25 - x20 - x31 =E= 0;
e10.. 0.92762181422141*x10**0.25 - x21 - x32 =E= 0;
e11.. 0.948415999107521*x11**0.25 - x22 - x33 =E= 0;
e12.. - x1 + x2 - x23 =E= 0;
e13.. - x2 + x3 - x24 =E= 0;
e14.. - x3 + x4 - x25 =E= 0;
e15.. - x4 + x5 - x26 =E= 0;
e16.. - x5 + x6 - x27 =E= 0;
e17.. - x6 + x7 - x28 =E= 0;
e18.. - x7 + x8 - x29 =E= 0;
e19.. - x8 + x9 - x30 =E= 0;
e20.. - x9 + x10 - x31 =E= 0;
e21.. - x10 + x11 - x32 =E= 0;
e22.. 0.03*x11 - x33 =L= 0;
e23.. - (0.95*log(x12) + 0.9025*log(x13) + 0.857375*log(x14) + 0.81450625*log(
x15) + 0.7737809375*log(x16) + 0.735091890625*log(x17) + 0.69833729609375
*log(x18) + 0.663420431289062*log(x19) + 0.630249409724609*log(x20) +
0.598736939238379*log(x21) + 11.3760018455292*log(x22)) - objvar =E= 0;
* set non default bounds
x1.fx = 3;
x2.lo = 3;
x3.lo = 3;
x4.lo = 3;
x5.lo = 3;
x6.lo = 3;
x7.lo = 3;
x8.lo = 3;
x9.lo = 3;
x10.lo = 3;
x11.lo = 3;
x12.lo = 0.95;
x13.lo = 0.95;
x14.lo = 0.95;
x15.lo = 0.95;
x16.lo = 0.95;
x17.lo = 0.95;
x18.lo = 0.95;
x19.lo = 0.95;
x20.lo = 0.95;
x21.lo = 0.95;
x22.lo = 0.95;
x23.fx = 0.05;
x24.lo = 0.05; x24.up = 0.0575;
x25.lo = 0.05; x25.up = 0.066125;
x26.lo = 0.05; x26.up = 0.07604375;
x27.lo = 0.05; x27.up = 0.0874503125;
x28.lo = 0.05; x28.up = 0.100567859375;
x29.lo = 0.05; x29.up = 0.11565303828125;
x30.lo = 0.05; x30.up = 0.133000994023437;
x31.lo = 0.05; x31.up = 0.152951143126953;
x32.lo = 0.05; x32.up = 0.175893814595996;
x33.lo = 0.05; x33.up = 0.202277886785395;
* set non default levels
* set non default marginals
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
Solve m using NLP minimizing objvar;
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