MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance ex2_1_7

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-4150.41013400 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-4150.41013800 (ANTIGONE) -4150.41014800 (BARON) -4150.41029200 (COUENNE) -4150.41013400 (CPLEX) -4150.41013400 (GUROBI) -4150.41013400 (LINDO) -4150.41013500 (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.
Sourceⓘ	Test Problem ex2.1.7 of Chapter 2 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QP
#Variablesⓘ	20
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	20
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	concave
#Nonzeros in Objectiveⓘ	20
#Nonlinear Nonzeros in Objectiveⓘ	20
#Constraintsⓘ	10
#Linear Constraintsⓘ	10
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	164
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	20
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	20
#Blocks in Hessian of Lagrangianⓘ	20
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	1
Average blocksize in Hessian of Lagrangianⓘ	1.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	5.0000e-01
Maximal coefficientⓘ	2.0000e+01
Infeasibility of initial pointⓘ	0.01396
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         11        1        0       10        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         21       21        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        185      165       20        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,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11;


e1.. 0.5*(sqr((-2) + x1) + 2*sqr((-2) + x2) + 3*sqr((-2) + x3) + 4*sqr((-2) + 
     x4) + 5*sqr((-2) + x5) + 6*sqr((-2) + x6) + 7*sqr((-2) + x7) + 8*sqr((-2)
      + x8) + 9*sqr((-2) + x9) + 10*sqr((-2) + x10) + 11*sqr((-2) + x11) + 12*
     sqr((-2) + x12) + 13*sqr((-2) + x13) + 14*sqr((-2) + x14) + 15*sqr((-2) + 
     x15) + 16*sqr((-2) + x16) + 17*sqr((-2) + x17) + 18*sqr((-2) + x18) + 19*
     sqr((-2) + x19) + 20*sqr((-2) + x20)) + objvar =E= 0;

e2..  - 3*x1 + 7*x2 - 5*x4 + x5 + x6 + 2*x8 - x9 - x10 - 9*x11 + 3*x12 + 5*x13
      + x16 + 7*x17 - 7*x18 - 4*x19 - 6*x20 =L= -5;

e3..    7*x1 - 5*x3 + x4 + x5 + 2*x7 - x8 - x9 - 9*x10 + 3*x11 + 5*x12 + x15
      + 7*x16 - 7*x17 - 4*x18 - 6*x19 - 3*x20 =L= 2;

e4..  - 5*x2 + x3 + x4 + 2*x6 - x7 - x8 - 9*x9 + 3*x10 + 5*x11 + x14 + 7*x15
      - 7*x16 - 4*x17 - 6*x18 - 3*x19 + 7*x20 =L= -1;

e5..  - 5*x1 + x2 + x3 + 2*x5 - x6 - x7 - 9*x8 + 3*x9 + 5*x10 + x13 + 7*x14
      - 7*x15 - 4*x16 - 6*x17 - 3*x18 + 7*x19 =L= -3;

e6..    x1 + x2 + 2*x4 - x5 - x6 - 9*x7 + 3*x8 + 5*x9 + x12 + 7*x13 - 7*x14
      - 4*x15 - 6*x16 - 3*x17 + 7*x18 - 5*x20 =L= 5;

e7..    x1 + 2*x3 - x4 - x5 - 9*x6 + 3*x7 + 5*x8 + x11 + 7*x12 - 7*x13 - 4*x14
      - 6*x15 - 3*x16 + 7*x17 - 5*x19 + x20 =L= 4;

e8..    2*x2 - x3 - x4 - 9*x5 + 3*x6 + 5*x7 + x10 + 7*x11 - 7*x12 - 4*x13
      - 6*x14 - 3*x15 + 7*x16 - 5*x18 + x19 + x20 =L= -1;

e9..    2*x1 - x2 - x3 - 9*x4 + 3*x5 + 5*x6 + x9 + 7*x10 - 7*x11 - 4*x12
      - 6*x13 - 3*x14 + 7*x15 - 5*x17 + x18 + x19 =L= 0;

e10..  - x1 - x2 - 9*x3 + 3*x4 + 5*x5 + x8 + 7*x9 - 7*x10 - 4*x11 - 6*x12
       - 3*x13 + 7*x14 - 5*x16 + x17 + x18 + 2*x20 =L= 9;

e11..    x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 + x12 + x13
       + x14 + x15 + x16 + x17 + x18 + x19 + x20 =L= 40;

* set non-default levels
x3.l = 1.04289;
x11.l = 1.74674;
x13.l = 0.43147;
x16.l = 4.43305;
x18.l = 15.85893;
x20.l = 16.4889;

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;