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)
350.52479410 p1 ( gdx sol )
(infeas: 6e-11)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-05-24 Git hash: 1198c186
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