MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance ex5_3_2

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.86415946 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1.86415946 (ANTIGONE) 1.86415946 (BARON) 1.86415946 (COUENNE) 1.86415944 (GUROBI) 1.86415946 (LINDO) 1.86415946 (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. Visweswaran, V and Floudas, C A, Computational Results for an Efficient Implementation of the GOP Algorithm and its Variants. Chapter 4 in Grossmann, I E, Ed, Global Optimization in Engineering Design, Kluwer Books, 1996, 111-153.
Sourceⓘ	Test Problem ex5.3.2 of Chapter 5 of Floudas e.a. handbook
Added to libraryⓘ	31 Jul 2001
Problem typeⓘ	QCP
#Variablesⓘ	22
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	10
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	4
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	16
#Linear Constraintsⓘ	7
#Quadratic Constraintsⓘ	9
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	59
#Nonlinear Nonzeros in Jacobianⓘ	24
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	24
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	4.3200e-03
Maximal coefficientⓘ	1.0000e+00
Infeasibility of initial pointⓘ	300
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         17       17        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
*         64       40       24        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  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17;


e1..    x1 + x2 + x3 + x4 =E= 300;

e2..    x5 - x6 - x7 =E= 0;

e3..    x8 - x9 - x10 - x11 =E= 0;

e4..    x12 - x13 - x14 - x15 =E= 0;

e5..    x16 - x17 - x18 =E= 0;

e6.. x13*x21 + 0.333*x1 - x5 =E= 0;

e7.. x13*x22 - x8*x20 + 0.333*x1 =E= 0;

e8.. -x8*x19 + 0.333*x1 =E= 0;

e9.. -x12*x21 - 0.333*x2 =E= 0;

e10.. x9*x20 - x12*x22 + 0.333*x2 =E= 0;

e11.. x9*x19 + 0.333*x2 - x16 =E= 0;

e12.. x14*x21 + 0.333*x3 + x6 =E= 30;

e13.. x10*x20 + x14*x22 + 0.333*x3 =E= 50;

e14.. x10*x19 + 0.333*x3 + x17 =E= 30;

e15..    x19 + x20 =E= 1;

e16..    x21 + x22 =E= 1;

e17..  - 0.00432*x1 - 0.01517*x2 - 0.01517*x9 - 0.00432*x13 + objvar =E= 0.9979
      ;

* set non-default bounds
x1.up = 300;
x2.up = 300;
x3.up = 300;
x4.up = 300;
x5.up = 300;
x6.up = 300;
x7.up = 300;
x8.up = 300;
x9.up = 300;
x10.up = 300;
x11.up = 300;
x12.up = 300;
x13.up = 300;
x14.up = 300;
x15.up = 300;
x16.up = 300;
x17.up = 300;
x18.up = 300;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 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;