MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ball_mk3_20
A simple MINLP with a feasible set described by a ball. The basic model over which these variations are made is: min sum_i=1^n x_i s.t. sum_i=1^n (x_i - 0.5)^2 <= (n-1)/4 x integer between -1 and 1. Obvisouly, this problem is infeasible and has no solution. It can be shown that any outer-approximation based method will need 2^n linear inequalities to show infeasibility, see reference. In this instance, the ball is an empty ellipse, but the quadratic form is still diagonal.
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | -21.00000000 (ALPHAECP) inf (ANTIGONE) inf (BARON) -9.00843129 (BONMIN) inf (COUENNE) inf (CPLEX) inf (GUROBI) inf (LINDO) inf (SCIP) inf (SHOT) |
Referencesⓘ | Hijazi, Hassan, Bonami, Pierre, and Ouorou, Adam, An Outer-Inner Approximation for Separable Mixed-Integer Nonlinear Programs, INFORMS Journal on Computing, 26:1, 2014, 31-44. |
Sourceⓘ | Pierre Bonami |
Applicationⓘ | Geometry |
Added to libraryⓘ | 11 Sep 2017 |
Problem typeⓘ | IQCP |
#Variablesⓘ | 20 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 20 |
#Nonlinear Variablesⓘ | 20 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 20 |
Objective Senseⓘ | min |
Objective typeⓘ | linear |
Objective curvatureⓘ | linear |
#Nonzeros in Objectiveⓘ | 20 |
#Nonlinear Nonzeros in Objectiveⓘ | 0 |
#Constraintsⓘ | 1 |
#Linear Constraintsⓘ | 0 |
#Quadratic Constraintsⓘ | 1 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | convex |
#Nonzeros in Jacobianⓘ | 20 |
#Nonlinear Nonzeros in Jacobianⓘ | 20 |
#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ⓘ | 8.8922e-03 |
Maximal coefficientⓘ | 1.0000e+00 |
Infeasibility of initial pointⓘ | 0.0001 |
Sparsity Jacobianⓘ | ![]() |
Sparsity Hessian of Lagrangianⓘ | ![]() |
$offlisting * * Equation counts * Total E G L N X C B * 2 1 0 1 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 21 1 0 20 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 41 21 20 0 * * Solve m using MINLP minimizing objvar; Variables objvar,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18 ,i19,i20,i21; Integer Variables i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18 ,i19,i20,i21; Equations e1,e2; e1.. objvar + i2 + i3 + i4 + i5 + i6 + i7 + i8 + i9 + i10 + i11 + i12 + i13 + i14 + i15 + i16 + i17 + i18 + i19 + i20 + i21 =E= 0; e2.. 0.0560877535068921*sqr(i20) - 0.0560877535068921*i20 + 0.0234361418326102* sqr(i19) - 0.0234361418326102*i19 + 0.0804348252437088*sqr(i18) - 0.0804348252437088*i18 + 0.083180630465482*sqr(i17) - 0.083180630465482* i17 + 0.0168840147598981*sqr(i16) - 0.0168840147598981*i16 + 0.0642555768399037*sqr(i15) - 0.0642555768399037*i15 + 0.0515967329760445* sqr(i14) - 0.0515967329760445*i14 + 0.0291406913653282*sqr(i13) - 0.0291406913653282*i13 + 0.0358736092274657*sqr(i12) - 0.0358736092274657* i12 + 0.0403619397376071*sqr(i11) - 0.0403619397376071*i11 + 0.0604484044580273*sqr(i10) - 0.0604484044580273*i10 + 0.0534869191762675* sqr(i9) - 0.0534869191762675*i9 + 0.0820022096762534*sqr(i8) - 0.0820022096762534*i8 + 0.0369575272885052*sqr(i7) - 0.0369575272885052*i7 + 0.00889217633273991*sqr(i6) - 0.00889217633273991*i6 + 0.0674863595874412*sqr(i5) - 0.0674863595874412*i5 + 0.0436989257405813* sqr(i4) - 0.0436989257405813*i4 + 0.0218982155241878*sqr(i3) - 0.0218982155241878*i3 + 0.0699896991762921*sqr(i2) - 0.0699896991762921*i2 + 0.0738876470847639*sqr(i21) - 0.0738876470847639*i21 =L= -9.99999999999335E-5; * set non-default bounds i2.lo = -1; i2.up = 2; i3.lo = -1; i3.up = 2; i4.lo = -1; i4.up = 2; i5.lo = -1; i5.up = 2; i6.lo = -1; i6.up = 2; i7.lo = -1; i7.up = 2; i8.lo = -1; i8.up = 2; i9.lo = -1; i9.up = 2; i10.lo = -1; i10.up = 2; i11.lo = -1; i11.up = 2; i12.lo = -1; i12.up = 2; i13.lo = -1; i13.up = 2; i14.lo = -1; i14.up = 2; i15.lo = -1; i15.up = 2; i16.lo = -1; i16.up = 2; i17.lo = -1; i17.up = 2; i18.lo = -1; i18.up = 2; i19.lo = -1; i19.up = 2; i20.lo = -1; i20.up = 2; i21.lo = -1; i21.up = 2; Model m / all /; m.limrow=0; m.limcol=0; m.tolproj=0.0; $if NOT '%gams.u1%' == '' $include '%gams.u1%' $if not set MINLP $set MINLP MINLP Solve m using %MINLP% minimizing objvar;
Last updated: 2024-03-25 Git hash: 1dae024f