MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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

Removed Instance procsyn

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	2068.20055500 p1 ( gdx sol ) (infeas: 2e-15)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	2068.20055500 (ANTIGONE) 2068.20055300 (BARON) 2066.13362400 (COUENNE) 2068.20055500 (LINDO) 2068.20046000 (SCIP)
Referencesⓘ	Novak Pintaric, Zorka and Kravanja, Zdravko, A Novel Bi-Level Optimization Method for the Identification of Critical Points in Flow Sheet Synthesis under Uncertainty, 2012.
Sourceⓘ	Model_E2.gms from minlp.org model 143
Applicationⓘ	Process Flowsheets
Added to libraryⓘ	18 Aug 2014
Removed from libraryⓘ	16 Feb 2022
Removed becauseⓘ	Instance is continuous and convex.
Problem typeⓘ	NLP
#Variablesⓘ	20
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	20
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	20
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	27
#Linear Constraintsⓘ	9
#Quadratic Constraintsⓘ	9
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	9
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	convex
#Nonzeros in Jacobianⓘ	72
#Nonlinear Nonzeros in Jacobianⓘ	27
#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ⓘ	2.5000e-02
Maximal coefficientⓘ	3.0000e+00
Infeasibility of initial pointⓘ	22.5
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         28        1       18        9        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
*         93       64       29        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;

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;


e1.. -(0.05*(sqr(x1) + x2**3) + 0.175*(sqr(x1) + x2**3) + 0.025*(sqr(x1) + x2**
     3) + 0.1*(sqr(x1) + x2**3) + 0.35*(sqr(x1) + x2**3) + 0.05*(sqr(x1) + x2**
     3) + 0.05*(sqr(x1) + x2**3) + 0.175*(sqr(x1) + x2**3) + 0.025*(sqr(x1) + 
     x2**3)) - 0.15*x3 - 0.525*x4 - 0.075*x5 - 0.3*x6 - 1.05*x7 - 0.15*x8
      - 0.15*x9 - 0.525*x10 - 0.075*x11 - 0.1*x12 - 0.35*x13 - 0.05*x14
      - 0.2*x15 - 0.7*x16 - 0.1*x17 - 0.1*x18 - 0.35*x19 - 0.05*x20 + objvar
      =E= -3.2;

e2..    x1 - 2*x3 - 2*x12 =G= -1;

e3..    x1 - 2*x4 - 2*x13 =G= -1;

e4..    x1 - 2*x5 - 2*x14 =G= -1;

e5..    x1 - 2*x6 - 2*x15 =G= -3;

e6..    x1 - 2*x7 - 2*x16 =G= -3;

e7..    x1 - 2*x8 - 2*x17 =G= -3;

e8..    x1 - 2*x9 - 2*x18 =G= -5;

e9..    x1 - 2*x10 - 2*x19 =G= -5;

e10..    x1 - 2*x11 - 2*x20 =G= -5;

e11.. -(1/x3 + sqr(x12)) + x2 =G= 2.5;

e12.. -(1/x4 + sqr(x13)) + x2 =G= 6.5;

e13.. -(1/x5 + sqr(x14)) + x2 =G= 10.5;

e14.. -(1/x6 + sqr(x15)) + x2 =G= 3.5;

e15.. -(1/x7 + sqr(x16)) + x2 =G= 7.5;

e16.. -(1/x8 + sqr(x17)) + x2 =G= 11.5;

e17.. -(1/x9 + sqr(x18)) + x2 =G= 4.5;

e18.. -(1/x10 + sqr(x19)) + x2 =G= 8.5;

e19.. -(1/x11 + sqr(x20)) + x2 =G= 12.5;

e20.. sqr(x3) + 2*x12 =L= 30;

e21.. sqr(x4) + 2*x13 =L= 30;

e22.. sqr(x5) + 2*x14 =L= 30;

e23.. sqr(x6) + 2*x15 =L= 30;

e24.. sqr(x7) + 2*x16 =L= 30;

e25.. sqr(x8) + 2*x17 =L= 30;

e26.. sqr(x9) + 2*x18 =L= 30;

e27.. sqr(x10) + 2*x19 =L= 30;

e28.. sqr(x11) + 2*x20 =L= 30;

* set non-default bounds
x3.up = 10;
x4.up = 10;
x5.up = 10;
x6.up = 10;
x7.up = 10;
x8.up = 10;
x9.up = 10;
x10.up = 10;
x11.up = 10;

* set non-default levels
x3.l = 0.1;
x4.l = 0.1;
x5.l = 0.1;
x6.l = 0.1;
x7.l = 0.1;
x8.l = 0.1;
x9.l = 0.1;
x10.l = 0.1;
x11.l = 0.1;

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;