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Instance ex8_3_13
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -49.93994239 (ANTIGONE) -43.08947820 (BARON) -100.00000000 (COUENNE) -49.84322832 (GUROBI) -100.00000000 (LINDO) -100.00000000 (SCIP) |
| Referencesⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. Schweiger, C A and Floudas, C A, Optimization Framework for the Synthesis of Chemical Reactor Networks, Industrial and Engineering Chemistry Research, 38:3, 1998, 744-766. |
| Sourceⓘ | Test Problem ex8.3.13 of Chapter 8 of Floudas e.a. handbook |
| Added to libraryⓘ | 31 Jul 2001 |
| Problem typeⓘ | NLP |
| #Variablesⓘ | 115 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 105 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 6 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 72 |
| #Linear Constraintsⓘ | 18 |
| #Quadratic Constraintsⓘ | 44 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 10 |
| Operands in Gen. Nonlin. Functionsⓘ | div exp mul vcpower |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 569 |
| #Nonlinear Nonzeros in Jacobianⓘ | 448 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 393 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 15 |
| #Blocks in Hessian of Lagrangianⓘ | 16 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 12 |
| Average blocksize in Hessian of Lagrangianⓘ | 6.5625 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 3.0000e-01 |
| Maximal coefficientⓘ | 5.4000e+07 |
| Infeasibility of initial pointⓘ | 300 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 73 73 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 116 116 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 576 128 448 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,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,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
,x116;
Positive Variables 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,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101
,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116;
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;
e1.. - objvar - 100*x95 + x97 + x98 + x99 + x100 + x101 =E= 0;
e2.. - x2 - x3 - x4 - x5 - x6 =E= -50;
e3.. - x7 - x8 - x9 - x10 - x11 =E= -50;
e4.. - x2 - x7 + x12 - x62 - x67 - x72 - x77 - x82 =E= 0;
e5.. - x3 - x8 + x13 - x63 - x68 - x73 - x78 - x83 =E= 0;
e6.. - x4 - x9 + x14 - x64 - x69 - x74 - x79 - x84 =E= 0;
e7.. - x5 - x10 + x15 - x65 - x70 - x75 - x80 - x85 =E= 0;
e8.. - x6 - x11 + x16 - x66 - x71 - x76 - x81 - x86 =E= 0;
e9.. x17*x12 - (x42*x62 + x46*x67 + x50*x72 + x54*x77 + x58*x82) - x2 =E= 0;
e10.. x18*x12 - (x43*x62 + x47*x67 + x51*x72 + x55*x77 + x59*x82) - x7 =E= 0;
e11.. x19*x12 - (x44*x62 + x48*x67 + x52*x72 + x56*x77 + x60*x82) =E= 0;
e12.. x20*x12 - (x45*x62 + x49*x67 + x53*x72 + x57*x77 + x61*x82) =E= 0;
e13.. x21*x13 - (x42*x63 + x46*x68 + x50*x73 + x54*x78 + x58*x83) - x3 =E= 0;
e14.. x22*x13 - (x43*x63 + x47*x68 + x51*x73 + x55*x78 + x59*x83) - x8 =E= 0;
e15.. x23*x13 - (x44*x63 + x48*x68 + x52*x73 + x56*x78 + x60*x83) =E= 0;
e16.. x24*x13 - (x45*x63 + x49*x68 + x53*x73 + x57*x78 + x61*x83) =E= 0;
e17.. x25*x14 - (x42*x64 + x46*x69 + x50*x74 + x54*x79 + x58*x84) - x4 =E= 0;
e18.. x26*x14 - (x43*x64 + x47*x69 + x51*x74 + x55*x79 + x59*x84) - x9 =E= 0;
e19.. x27*x14 - (x44*x64 + x48*x69 + x52*x74 + x56*x79 + x60*x84) =E= 0;
e20.. x28*x14 - (x45*x64 + x49*x69 + x53*x74 + x57*x79 + x61*x84) =E= 0;
e21.. x29*x15 - (x42*x65 + x46*x70 + x50*x75 + x54*x80 + x58*x85) - x5 =E= 0;
e22.. x30*x15 - (x43*x65 + x47*x70 + x51*x75 + x55*x80 + x59*x85) - x10 =E= 0;
e23.. x31*x15 - (x44*x65 + x48*x70 + x52*x75 + x56*x80 + x60*x85) =E= 0;
e24.. x32*x15 - (x45*x65 + x49*x70 + x53*x75 + x57*x80 + x61*x85) =E= 0;
e25.. x33*x16 - (x42*x66 + x46*x71 + x50*x76 + x54*x81 + x58*x86) - x6 =E= 0;
e26.. x34*x16 - (x43*x66 + x47*x71 + x51*x76 + x55*x81 + x59*x86) - x11 =E= 0;
e27.. x35*x16 - (x44*x66 + x48*x71 + x52*x76 + x56*x81 + x60*x86) =E= 0;
e28.. x36*x16 - (x45*x66 + x49*x71 + x53*x76 + x57*x81 + x61*x86) =E= 0;
e29.. - x12 + x37 =E= 0;
e30.. - x13 + x38 =E= 0;
e31.. - x14 + x39 =E= 0;
e32.. - x15 + x40 =E= 0;
e33.. - x16 + x41 =E= 0;
e34.. x42*x37 - (x17*x12 + x97*(-x107 - x108)) =E= 0;
e35.. x43*x37 - (x18*x12 + x97*(-x107 - x108)) =E= 0;
e36.. x44*x37 - (x19*x12 + x97*x107) =E= 0;
e37.. x45*x37 - (x20*x12 + x97*x108) =E= 0;
e38.. x46*x38 - (x21*x13 + x98*(-x109 - x110)) =E= 0;
e39.. x47*x38 - (x22*x13 + x98*(-x109 - x110)) =E= 0;
e40.. x48*x38 - (x23*x13 + x98*x109) =E= 0;
e41.. x49*x38 - (x24*x13 + x98*x110) =E= 0;
e42.. x50*x39 - (x25*x14 + x99*(-x111 - x112)) =E= 0;
e43.. x51*x39 - (x26*x14 + x99*(-x111 - x112)) =E= 0;
e44.. x52*x39 - (x27*x14 + x99*x111) =E= 0;
e45.. x53*x39 - (x28*x14 + x99*x112) =E= 0;
e46.. x54*x40 - (x29*x15 + x100*(-x113 - x114)) =E= 0;
e47.. x55*x40 - (x30*x15 + x100*(-x113 - x114)) =E= 0;
e48.. x56*x40 - (x31*x15 + x100*x113) =E= 0;
e49.. x57*x40 - (x32*x15 + x100*x114) =E= 0;
e50.. x58*x41 - (x33*x16 + x101*(-x115 - x116)) =E= 0;
e51.. x59*x41 - (x34*x16 + x101*(-x115 - x116)) =E= 0;
e52.. x60*x41 - (x35*x16 + x101*x115) =E= 0;
e53.. x61*x41 - (x36*x16 + x101*x116) =E= 0;
e54.. -54000000*exp(-9631.60543532964/x102)*x42*x43**0.3 + x107 =E= 0;
e55.. -54000000*exp(-9631.60543532964/x103)*x46*x47**0.3 + x109 =E= 0;
e56.. -54000000*exp(-9631.60543532964/x104)*x50*x51**0.3 + x111 =E= 0;
e57.. -54000000*exp(-9631.60543532964/x105)*x54*x55**0.3 + x113 =E= 0;
e58.. -54000000*exp(-9631.60543532964/x106)*x58*x59**0.3 + x115 =E= 0;
e59.. -360000*exp(-4815.80271766482/x102)*x42**0.5*x43**1.8 + x108 =E= 0;
e60.. -360000*exp(-4815.80271766482/x103)*x46**0.5*x47**1.8 + x110 =E= 0;
e61.. -360000*exp(-4815.80271766482/x104)*x50**0.5*x51**1.8 + x112 =E= 0;
e62.. -360000*exp(-4815.80271766482/x105)*x54**0.5*x55**1.8 + x114 =E= 0;
e63.. -360000*exp(-4815.80271766482/x106)*x58**0.5*x59**1.8 + x116 =E= 0;
e64.. x37 - x62 - x63 - x64 - x65 - x66 - x87 =E= 0;
e65.. x38 - x67 - x68 - x69 - x70 - x71 - x88 =E= 0;
e66.. x39 - x72 - x73 - x74 - x75 - x76 - x89 =E= 0;
e67.. x40 - x77 - x78 - x79 - x80 - x81 - x90 =E= 0;
e68.. x41 - x82 - x83 - x84 - x85 - x86 - x91 =E= 0;
e69.. - x87 - x88 - x89 - x90 - x91 + x92 =E= 0;
e70.. x92*x93 - (x87*x42 + x88*x46 + x89*x50 + x90*x54 + x91*x58) =E= 0;
e71.. x92*x94 - (x87*x43 + x88*x47 + x89*x51 + x90*x55 + x91*x59) =E= 0;
e72.. x92*x95 - (x87*x44 + x88*x48 + x89*x52 + x90*x56 + x91*x60) =E= 0;
e73.. x92*x96 - (x87*x45 + x88*x49 + x89*x53 + x90*x57 + x91*x61) =E= 0;
* set non-default bounds
x2.up = 1000;
x3.up = 1000;
x4.up = 1000;
x5.up = 1000;
x6.up = 1000;
x7.up = 1000;
x8.up = 1000;
x9.up = 1000;
x10.up = 1000;
x11.up = 1000;
x12.up = 1000;
x13.up = 1000;
x14.up = 1000;
x15.up = 1000;
x16.up = 1000;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1000;
x38.up = 1000;
x39.up = 1000;
x40.up = 1000;
x41.up = 1000;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1000;
x63.up = 1000;
x64.up = 1000;
x65.up = 1000;
x66.up = 1000;
x67.up = 1000;
x68.up = 1000;
x69.up = 1000;
x70.up = 1000;
x71.up = 1000;
x72.up = 1000;
x73.up = 1000;
x74.up = 1000;
x75.up = 1000;
x76.up = 1000;
x77.up = 1000;
x78.up = 1000;
x79.up = 1000;
x80.up = 1000;
x81.up = 1000;
x82.up = 1000;
x83.up = 1000;
x84.up = 1000;
x85.up = 1000;
x86.up = 1000;
x87.up = 1000;
x88.up = 1000;
x89.up = 1000;
x90.up = 1000;
x91.up = 1000;
x92.up = 1000;
x93.up = 1;
x94.up = 1;
x95.up = 1;
x96.up = 1;
x97.up = 10000;
x98.up = 10000;
x99.up = 10000;
x100.up = 10000;
x101.up = 10000;
x102.lo = 300; x102.up = 800;
x103.lo = 300; x103.up = 800;
x104.lo = 300; x104.up = 800;
x105.lo = 300; x105.up = 800;
x106.lo = 300; x106.up = 800;
x107.up = 10000;
x108.up = 10000;
x109.up = 10000;
x110.up = 10000;
x111.up = 10000;
x112.up = 10000;
x113.up = 10000;
x114.up = 10000;
x115.up = 10000;
x116.up = 10000;
* set non-default levels
x2.l = 50;
x3.l = 50;
x4.l = 50;
x5.l = 50;
x6.l = 50;
x7.l = 50;
x8.l = 50;
x9.l = 50;
x10.l = 50;
x11.l = 50;
x12.l = 50;
x13.l = 50;
x14.l = 50;
x15.l = 50;
x16.l = 50;
x17.l = 0.2;
x18.l = 0.2;
x19.l = 0.2;
x20.l = 0.2;
x21.l = 0.2;
x22.l = 0.2;
x23.l = 0.2;
x24.l = 0.2;
x25.l = 0.2;
x26.l = 0.2;
x27.l = 0.2;
x28.l = 0.2;
x29.l = 0.2;
x30.l = 0.2;
x31.l = 0.2;
x32.l = 0.2;
x33.l = 0.2;
x34.l = 0.2;
x35.l = 0.2;
x36.l = 0.2;
x37.l = 100;
x38.l = 100;
x39.l = 100;
x40.l = 100;
x41.l = 100;
x42.l = 0.2;
x43.l = 0.2;
x44.l = 0.2;
x45.l = 0.2;
x46.l = 0.2;
x47.l = 0.2;
x48.l = 0.2;
x49.l = 0.2;
x50.l = 0.2;
x51.l = 0.2;
x52.l = 0.2;
x53.l = 0.2;
x54.l = 0.2;
x55.l = 0.2;
x56.l = 0.2;
x57.l = 0.2;
x58.l = 0.2;
x59.l = 0.2;
x60.l = 0.2;
x61.l = 0.2;
x62.l = 50;
x63.l = 50;
x64.l = 50;
x65.l = 50;
x66.l = 50;
x67.l = 50;
x68.l = 50;
x69.l = 50;
x70.l = 50;
x71.l = 50;
x72.l = 50;
x73.l = 50;
x74.l = 50;
x75.l = 50;
x76.l = 50;
x77.l = 50;
x78.l = 50;
x79.l = 50;
x80.l = 50;
x81.l = 50;
x82.l = 50;
x83.l = 50;
x84.l = 50;
x85.l = 50;
x86.l = 50;
x87.l = 50;
x88.l = 50;
x89.l = 50;
x90.l = 50;
x91.l = 50;
x92.l = 100;
x93.l = 0.2;
x94.l = 0.2;
x95.l = 0.2;
x96.l = 0.2;
x97.l = 1;
x98.l = 1;
x99.l = 1;
x100.l = 1;
x101.l = 1;
x102.l = 400;
x103.l = 400;
x104.l = 400;
x105.l = 400;
x106.l = 400;
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