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Instance ex8_4_1

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.61857276 p1 ( gdx sol ) (infeas: 3e-10)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.61857107 (ANTIGONE) 0.61857276 (BARON) 0.61857276 (COUENNE) 0.61857254 (GUROBI) 0.61857239 (LINDO) 0.61857121 (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. Esposito, W R and Floudas, C A, Global Optimization in Parameter Estimation of Nonlinear Algebraic Models via the Error-in-Variables Approach, Industrial and Engineering Chemistry Research, 37:5, 1998, 1841-1858. Tjoa, I B and Biegler, L T, Reduced Successive Quadratic Programming Strategy for Errors-in-Variables Estimation, Computers and Chemical Engineering, 16:6, 1992, 523-533.
Sourceⓘ	Test Problem ex8.4.1 of Chapter 8 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCQP
#Variablesⓘ	22
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	21
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	20
#Nonlinear Nonzeros in Objectiveⓘ	20
#Constraintsⓘ	10
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	10
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	40
#Nonlinear Nonzeros in Jacobianⓘ	20
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	40
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	20
#Blocks in Hessian of Lagrangianⓘ	11
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	11
Average blocksize in Hessian of Lagrangianⓘ	1.909091
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	9.0000e-01
Maximal coefficientⓘ	7.4000e+00
Infeasibility of initial pointⓘ	3.092
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         11       11        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         23       23        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         61       21       40        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,objvar;

Positive Variables  x21;

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


e1.. -(sqr(x1) + sqr((-5.9) + x2) + sqr((-0.9) + x3) + sqr((-5.4) + x4) + sqr((
     -1.8) + x5) + sqr((-4.4) + x6) + sqr((-2.6) + x7) + sqr((-4.6) + x8) + 
     sqr((-3.3) + x9) + sqr((-3.5) + x10) + sqr((-4.4) + x11) + sqr((-3.7) + 
     x12) + sqr((-5.2) + x13) + sqr((-2.8) + x14) + sqr((-6.1) + x15) + sqr((-
     2.8) + x16) + sqr((-6.5) + x17) + sqr((-2.4) + x18) + sqr((-7.4) + x19) + 
     sqr((-1.5) + x20)) + objvar =E= 0;

e2.. x22*x1 - x2 + x21 =E= 0;

e3.. x22*x3 - x4 + x21 =E= 0;

e4.. x22*x5 - x6 + x21 =E= 0;

e5.. x22*x7 - x8 + x21 =E= 0;

e6.. x22*x9 - x10 + x21 =E= 0;

e7.. x22*x11 - x12 + x21 =E= 0;

e8.. x22*x13 - x14 + x21 =E= 0;

e9.. x22*x15 - x16 + x21 =E= 0;

e10.. x22*x17 - x18 + x21 =E= 0;

e11.. x22*x19 - x20 + x21 =E= 0;

* set non-default bounds
x1.lo = -0.5; x1.up = 0.5;
x2.lo = 5.4; x2.up = 6.4;
x3.lo = 0.4; x3.up = 1.4;
x4.lo = 4.9; x4.up = 5.9;
x5.lo = 1.3; x5.up = 2.3;
x6.lo = 3.9; x6.up = 4.9;
x7.lo = 2.1; x7.up = 3.1;
x8.lo = 4.1; x8.up = 5.1;
x9.lo = 2.8; x9.up = 3.8;
x10.lo = 3; x10.up = 4;
x11.lo = 3.9; x11.up = 4.9;
x12.lo = 3.2; x12.up = 4.2;
x13.lo = 4.7; x13.up = 5.7;
x14.lo = 2.3; x14.up = 3.3;
x15.lo = 5.6; x15.up = 6.6;
x16.lo = 2.3; x16.up = 3.3;
x17.lo = 6; x17.up = 7;
x18.lo = 1.9; x18.up = 2.9;
x19.lo = 6.9; x19.up = 7.9;
x20.lo = 1; x20.up = 2;
x21.up = 10;
x22.lo = -2; x22.up = 2;

* set non-default levels
x1.l = -0.328252868;
x2.l = 6.243266708;
x3.l = 0.950375356;
x4.l = 5.201137904;
x5.l = 1.592212117;
x6.l = 4.124052867;
x7.l = 2.449830504;
x8.l = 4.956270347;
x9.l = 2.867113723;
x10.l = 3.500210669;
x11.l = 4.898117627;
x12.l = 3.778733378;
x13.l = 5.691133039;
x14.l = 3.062250467;
x15.l = 5.730692483;
x16.l = 2.939718759;
x17.l = 6.159517864;
x18.l = 2.150080533;
x19.l = 7.568928609;
x20.l = 1.435356381;
x21.l = 3.59700266;
x22.l = -0.594234528;

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;