MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance nvs12
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | -481.20000000 (ALPHAECP) -481.20000000 (ANTIGONE) -481.20000000 (BARON) -481.20000000 (BONMIN) -481.20000000 (COUENNE) -481.20000020 (CPLEX) -481.20000000 (GUROBI) -481.20000000 (LINDO) -481.20000000 (SCIP) -481.20004800 (SHOT) |
Referencesⓘ | Gupta, Omprakash K and Ravindran, A, Branch and Bound Experiments in Convex Nonlinear Integer Programming, Management Science, 13:12, 1985, 1533-1546. Tawarmalani, M and Sahinidis, N V, Exact Algorithms for Global Optimization of Mixed-Integer Nonlinear Programs. In Pardalos, Panos M and Romeijn, H Edwin, Eds, Handbook of Global Optimization - Volume 2: Heuristic Approaches, Kluwer Academic Publishers, 65-85. Tawarmalani, M and Sahinidis, N V, Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming: Theory, Algorithms, Software, and Applications, Kluwer, 2002. |
Sourceⓘ | BARON book instance gupta/gupta12 |
Added to libraryⓘ | 25 Jul 2002 |
Problem typeⓘ | IQCQP |
#Variablesⓘ | 4 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 4 |
#Nonlinear Variablesⓘ | 4 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 4 |
Objective Senseⓘ | min |
Objective typeⓘ | quadratic |
Objective curvatureⓘ | convex |
#Nonzeros in Objectiveⓘ | 4 |
#Nonlinear Nonzeros in Objectiveⓘ | 4 |
#Constraintsⓘ | 4 |
#Linear Constraintsⓘ | 0 |
#Quadratic Constraintsⓘ | 4 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | convex |
#Nonzeros in Jacobianⓘ | 16 |
#Nonlinear Nonzeros in Jacobianⓘ | 16 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 16 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 4 |
#Blocks in Hessian of Lagrangianⓘ | 1 |
Minimal blocksize in Hessian of Lagrangianⓘ | 4 |
Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
Average blocksize in Hessian of Lagrangianⓘ | 4.0 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 2.0000e+00 |
Maximal coefficientⓘ | 9.3200e+01 |
Infeasibility of initial pointⓘ | 0 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 5 1 4 0 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 5 1 0 4 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 21 1 20 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,objvar; Integer Variables i1,i2,i3,i4; Equations e1,e2,e3,e4,e5; e1.. (-9*sqr(i1)) - 10*i1*i2 - 8*sqr(i2) - 5*sqr(i3) - 6*i3*i1 - 10*i3*i2 - 7* sqr(i4) - 10*i4*i1 - 6*i4*i2 - 2*i4*i3 =G= -1100; e2.. (-6*sqr(i1)) - 8*i1*i2 - 6*sqr(i2) - 4*sqr(i3) - 2*i3*i1 - 2*i3*i2 - 8* sqr(i4) + 2*i4*i1 + 10*i4*i2 =G= -440; e3.. (-9*sqr(i1)) - 6*sqr(i2) - 8*sqr(i3) + 2*i2*i1 + 2*i3*i2 - 6*sqr(i4) + 4* i4*i1 + 4*i4*i2 - 2*i4*i3 =G= -310; e4.. (-8*sqr(i1)) - 4*sqr(i2) - 9*sqr(i3) - 7*sqr(i4) - 2*i2*i1 - 2*i3*i1 - 4* i3*i2 + 6*i4*i1 + 2*i4*i2 - 2*i4*i3 =G= -460; e5.. -(7*sqr(i1) + 6*sqr(i2) - 20*i1 - 93.2*i2 + 8*sqr(i3) - 6*i3*i1 + 4*i3*i2 - 67.2*i3 + 6*sqr(i4) + 2*i4*i1 + 2*i4*i3 - 36.6*i4) + objvar =E= 0; * set non-default bounds i1.up = 200; i2.up = 200; i3.up = 200; i4.up = 200; * set non-default levels i1.l = 1; i2.l = 1; i3.l = 1; i4.l = 1; 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: 2024-08-26 Git hash: 6cc1607f