MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance lakes
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 350.52479380 (ANTIGONE) 350.52150700 (BARON) 350.52479410 (LINDO) 350.51782350 (SCIP) |
| Sourceⓘ | CUTE model lakes |
| Applicationⓘ | Water Resource Management |
| Added to libraryⓘ | 06 Feb 2017 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 90 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 90 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 60 |
| #Nonlinear Nonzeros in Objectiveⓘ | 60 |
| #Constraintsⓘ | 78 |
| #Linear Constraintsⓘ | 60 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 18 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 240 |
| #Nonlinear Nonzeros in Jacobianⓘ | 30 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 114 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 90 |
| #Blocks in Hessian of Lagrangianⓘ | 78 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.153846 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 5.5655e+05 |
| Infeasibility of initial pointⓘ | 551.1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 79 79 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 91 91 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 301 211 90 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,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,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,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79;
e1.. - x19 + x20 + x31 =E= -22;
e2.. - x20 - x21 + x22 + x33 =E= -1;
e3.. - x22 - x23 + x24 + x35 =E= 3;
e4.. - x24 - x25 + x26 + x37 =E= -27.2;
e5.. - x26 - x27 + x28 + x39 =E= 51.5;
e6.. - x31 + x32 + x43 =E= 44;
e7.. - x32 - x33 + x34 + x45 =E= 162;
e8.. - x34 - x35 + x36 + x47 =E= 8;
e9.. - x36 - x37 + x38 + x49 =E= 12.5;
e10.. - x38 - x39 + x40 + x51 =E= 53.5;
e11.. - x43 + x44 + x55 =E= -11;
e12.. - x44 - x45 + x46 + x57 =E= 60;
e13.. - x46 - x47 + x48 + x59 =E= 10;
e14.. - x48 - x49 + x50 + x61 =E= 18;
e15.. - x50 - x51 + x52 + x63 =E= 39;
e16.. - x55 + x56 + x67 =E= 124;
e17.. - x56 - x57 + x58 + x69 =E= 246;
e18.. - x58 - x59 + x60 + x71 =E= 6;
e19.. - x60 - x61 + x62 + x73 =E= 9.7;
e20.. - x62 - x63 + x64 + x75 =E= 17.2;
e21.. - x67 + x68 + x79 =E= 127;
e22.. - x68 - x69 + x70 + x81 =E= 175;
e23.. - x70 - x71 + x72 + x83 =E= 3;
e24.. - x72 - x73 + x74 + x85 =E= 10;
e25.. - x74 - x75 + x76 + x87 =E= 30.2;
e26.. x19 - x79 + x80 =E= 78;
e27.. x21 - x80 - x81 + x82 =E= 156;
e28.. x23 - x82 - x83 + x84 =E= 3;
e29.. x25 - x84 - x85 + x86 =E= 14;
e30.. x27 - x86 - x87 + x88 =E= 23.2;
e31.. 0.0841168*sqr(x29)*sqrt(x1) - x22 =E= 0;
e32.. 0.1280849*sqr(x30)*sqrt(x2) - x24 =E= 0;
e33.. 0.2605*x3**2.2 - x26 =E= 0;
e34.. 0.00103993344426*x21 + 0.1086956521739*x23 - x29 =E= 543.4;
e35.. - x1 + 0.002079866888519*x21 - 0.2173913043478*x23 =E= 0;
e36.. 0.2173913043478*x23 - x30 =E= 543.4;
e37.. - x2 + 0.2173913043478*x23 - 0.009510223490252*x25 =E= 0;
e38.. - x3 + 0.009510223490252*x25 =E= 550.11;
e39.. 0.0841168*sqr(x41)*sqrt(x4) - x34 =E= 0;
e40.. 0.1280849*sqr(x42)*sqrt(x5) - x36 =E= 0;
e41.. 0.2605*x6**2.2 - x38 =E= 0;
e42.. 0.00103993344426*x33 + 0.1086956521739*x35 - x41 =E= 543.4;
e43.. - x4 + 0.002079866888519*x33 - 0.2173913043478*x35 =E= 0;
e44.. 0.2173913043478*x35 - x42 =E= 543.4;
e45.. - x5 + 0.2173913043478*x35 - 0.009510223490252*x37 =E= 0;
e46.. - x6 + 0.009510223490252*x37 =E= 550.11;
e47.. 0.0841168*sqr(x53)*sqrt(x7) - x46 =E= 0;
e48.. 0.1280849*sqr(x54)*sqrt(x8) - x48 =E= 0;
e49.. 0.2605*x9**2.2 - x50 =E= 0;
e50.. 0.00103993344426*x45 + 0.1086956521739*x47 - x53 =E= 543.4;
e51.. - x7 + 0.002079866888519*x45 - 0.2173913043478*x47 =E= 0;
e52.. 0.2173913043478*x47 - x54 =E= 543.4;
e53.. - x8 + 0.2173913043478*x47 - 0.009510223490252*x49 =E= 0;
e54.. - x9 + 0.009510223490252*x49 =E= 550.11;
e55.. 0.0841168*sqr(x65)*sqrt(x10) - x58 =E= 0;
e56.. 0.1280849*sqr(x66)*sqrt(x11) - x60 =E= 0;
e57.. 0.2605*x12**2.2 - x62 =E= 0;
e58.. 0.00103993344426*x57 + 0.1086956521739*x59 - x65 =E= 543.4;
e59.. - x10 + 0.002079866888519*x57 - 0.2173913043478*x59 =E= 0;
e60.. 0.2173913043478*x59 - x66 =E= 543.4;
e61.. - x11 + 0.2173913043478*x59 - 0.009510223490252*x61 =E= 0;
e62.. - x12 + 0.009510223490252*x61 =E= 550.11;
e63.. 0.0841168*sqr(x77)*sqrt(x13) - x70 =E= 0;
e64.. 0.1280849*sqr(x78)*sqrt(x14) - x72 =E= 0;
e65.. 0.2605*x15**2.2 - x74 =E= 0;
e66.. 0.00103993344426*x69 + 0.1086956521739*x71 - x77 =E= 543.4;
e67.. - x13 + 0.002079866888519*x69 - 0.2173913043478*x71 =E= 0;
e68.. 0.2173913043478*x71 - x78 =E= 543.4;
e69.. - x14 + 0.2173913043478*x71 - 0.009510223490252*x73 =E= 0;
e70.. - x15 + 0.009510223490252*x73 =E= 550.11;
e71.. 0.0841168*sqr(x89)*sqrt(x16) - x82 =E= 0;
e72.. 0.1280849*sqr(x90)*sqrt(x17) - x84 =E= 0;
e73.. 0.2605*x18**2.2 - x86 =E= 0;
e74.. 0.00103993344426*x81 + 0.1086956521739*x83 - x89 =E= 543.4;
e75.. - x16 + 0.002079866888519*x81 - 0.2173913043478*x83 =E= 0;
e76.. 0.2173913043478*x83 - x90 =E= 543.4;
e77.. - x17 + 0.2173913043478*x83 - 0.009510223490252*x85 =E= 0;
e78.. - x18 + 0.009510223490252*x85 =E= 550.11;
e79.. 0.001*((464.504 - x20)*x20 + (405522.144 - x19)*x19 + (405407.292 - x31)*
x31 + (349.33 - x22)*x22 + (555583.632 - x21)*x21 + (555699.024 - x33)*
x33 + (361.078 - x24)*x24 + (5273.992 - x23)*x23 + (5276.2 - x35)*x35 + (
423.116 - x26)*x26 + (119974.047 - x25)*x25 + (119997.18 - x37)*x37 + (
464.504 - x28)*x28 + (38980.8 - x27)*x27 + (39110.4 - x39)*x39 + (167.578
- x32)*x32 + (405441.072 - x43)*x43 + (346.51 - x34)*x34 + (555910.576
- x45)*x45 + (359.834 - x36)*x36 + (5279.788 - x47)*x47 + (421.17 - x38)
*x38 + (120093.918 - x49)*x49 + (430.508 - x40)*x40 + (39195.2 - x51)*x51
+ (165.832 - x44)*x44 + (405616.728 - x55)*x55 + (347.442 - x46)*x46 + (
556208.672 - x57)*x57 + (365.352 - x48)*x48 + (5281.812 - x59)*x59 + (
415.676 - x50)*x50 + (120148.596 - x61)*x61 + (407.71 - x52)*x52 + (
39305.6 - x63)*x63 + (160.268 - x56)*x56 + (405832.92 - x67)*x67 + (
357.308 - x58)*x58 + (556449.072 - x69)*x69 + (371.834 - x60)*x60 + (
5282.916 - x71)*x71 + (412.832 - x62)*x62 + (120182.244 - x73)*x73 + (
372.616 - x64)*x64 + (39417.6 - x75)*x75 + (130.69 - x68)*x68 + (
405907.236 - x79)*x79 + (376.02 - x70)*x70 + (556554.848 - x81)*x81 + (
385.136 - x72)*x72 + (5282.916 - x83)*x83 + (408.6 - x74)*x74 + (
120165.42 - x85)*x85 + (402.2 - x76)*x76 + (39412.8 - x87)*x87 + (144.01
- x80)*x80 + (387.666 - x82)*x82 + (393.302 - x84)*x84 + (408.5 - x86)*
x86 + (482.158 - x88)*x88) + objvar =E= 734595853.838046;
* set non-default bounds
x1.lo = 0.0001;
x2.lo = 0.0001;
x3.lo = 0.0001;
x4.lo = 0.0001;
x5.lo = 0.0001;
x6.lo = 0.0001;
x7.lo = 0.0001;
x8.lo = 0.0001;
x9.lo = 0.0001;
x10.lo = 0.0001;
x11.lo = 0.0001;
x12.lo = 0.0001;
x13.lo = 0.0001;
x14.lo = 0.0001;
x15.lo = 0.0001;
x16.lo = 0.0001;
x17.lo = 0.0001;
x18.lo = 0.0001;
* set non-default levels
x1.l = 1;
x2.l = 1;
x3.l = 1;
x4.l = 1;
x5.l = 1;
x6.l = 1;
x7.l = 1;
x8.l = 1;
x9.l = 1;
x10.l = 1;
x11.l = 1;
x12.l = 1;
x13.l = 1;
x14.l = 1;
x15.l = 1;
x16.l = 1;
x17.l = 1;
x18.l = 1;
x19.l = 1;
x20.l = 1;
x21.l = 1;
x22.l = 1;
x23.l = 1;
x24.l = 1;
x25.l = 1;
x26.l = 1;
x27.l = 1;
x28.l = 1;
x29.l = 1;
x30.l = 1;
x31.l = 1;
x32.l = 1;
x33.l = 1;
x34.l = 1;
x35.l = 1;
x36.l = 1;
x37.l = 1;
x38.l = 1;
x39.l = 1;
x40.l = 1;
x41.l = 1;
x42.l = 1;
x43.l = 1;
x44.l = 1;
x45.l = 1;
x46.l = 1;
x47.l = 1;
x48.l = 1;
x49.l = 1;
x50.l = 1;
x51.l = 1;
x52.l = 1;
x53.l = 1;
x54.l = 1;
x55.l = 1;
x56.l = 1;
x57.l = 1;
x58.l = 1;
x59.l = 1;
x60.l = 1;
x61.l = 1;
x62.l = 1;
x63.l = 1;
x64.l = 1;
x65.l = 1;
x66.l = 1;
x67.l = 1;
x68.l = 1;
x69.l = 1;
x70.l = 1;
x71.l = 1;
x72.l = 1;
x73.l = 1;
x74.l = 1;
x75.l = 1;
x76.l = 1;
x77.l = 1;
x78.l = 1;
x79.l = 1;
x80.l = 1;
x81.l = 1;
x82.l = 1;
x83.l = 1;
x84.l = 1;
x85.l = 1;
x86.l = 1;
x87.l = 1;
x88.l = 1;
x89.l = 1;
x90.l = 1;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc