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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance st_e30

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-1.58113883 p1 ( gdx sol ) (infeas: 1e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-1.5811389 (ANTIGONE) -1.58113884 (BARON) -1.58113883 (COUENNE) -1.58113965 (GUROBI) -1.58113883 (LINDO) -1.58113894 (SCIP)
Referencesⓘ	Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. Marin, R, Points of location on a fixture, 1998. Personal Communication.
Sourceⓘ	BARON book instance misc/e30
Added to libraryⓘ	03 Sep 2002
Problem typeⓘ	QCP
#Variablesⓘ	14
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	7
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	15
#Linear Constraintsⓘ	10
#Quadratic Constraintsⓘ	5
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	42
#Nonlinear Nonzeros in Jacobianⓘ	14
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	14
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	2
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	4
Average blocksize in Hessian of Lagrangianⓘ	3.5
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	2.0000e+00
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         16        8        3        5        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         15       15        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         44       30       14        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,objvar;

Positive Variables  x11,x12,x13,x14;

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


e1.. -x12*x7 - x1 + x3 =E= 0;

e2.. -x12*x8 - x2 + x4 =E= 0;

e3.. (-x13*x7) - x11*x9 - x1 + x5 =E= 0;

e4.. (-x13*x8) - x11*x10 - x2 + x6 =E= 0;

e5.. sqr(x7) + sqr(x8) =E= 1;

e6..    x8 + x9 =E= 0;

e7..  - x7 + x10 =E= 0;

e8..  - x12 + x14 =L= 0;

e9..  - x11 + x14 =L= 0;

e10..    2*x1 + x2 =G= -1;

e11..    2*x3 + x4 =G= -1;

e12..    2*x5 + x6 =G= -1;

e13..    x1 + x2 =L= 1;

e14..    x3 + x4 =L= 1;

e15..    x5 + x6 =L= 1;

e16..    x14 + objvar =E= 0;

* set non-default bounds
x1.lo = -1; x1.up = 1;
x2.lo = -1; x2.up = 1;
x3.lo = -1; x3.up = 1;
x4.lo = -1; x4.up = 1;
x5.lo = -1; x5.up = 1;
x6.lo = -1; x6.up = 1;
x7.lo = -1; x7.up = 1;
x8.lo = -1; x8.up = 1;
x9.lo = -1; x9.up = 1;
x10.lo = -1; x10.up = 1;
x11.up = 3;
x12.up = 3;
x13.up = 3;
x14.up = 3;

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;