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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex2_1_5
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | -268.01463250 (ANTIGONE) -268.01463180 (BARON) -268.01463160 (COUENNE) -268.01463150 (CPLEX) -268.01463170 (GUROBI) -268.01463150 (LINDO) -268.01463860 (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. |
Sourceⓘ | Test Problem ex2.1.5 of Chapter 2 of Floudas e.a. handbook |
Added to libraryⓘ | 31 Jul 2001 |
Problem typeⓘ | QP |
#Variablesⓘ | 10 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 7 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 0 |
Objective Senseⓘ | min |
Objective typeⓘ | quadratic |
Objective curvatureⓘ | concave |
#Nonzeros in Objectiveⓘ | 10 |
#Nonlinear Nonzeros in Objectiveⓘ | 7 |
#Constraintsⓘ | 11 |
#Linear Constraintsⓘ | 11 |
#Quadratic Constraintsⓘ | 0 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | linear |
#Nonzeros in Jacobianⓘ | 101 |
#Nonlinear Nonzeros in Jacobianⓘ | 0 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 7 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 7 |
#Blocks in Hessian of Lagrangianⓘ | 7 |
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ⓘ | 5.0000e-01 |
Maximal coefficientⓘ | 9.0000e+01 |
Infeasibility of initial pointⓘ | 6e-05 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 12 1 0 11 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 11 11 0 0 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 112 105 7 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12; e1.. -(-0.5*(10*x1*x1 + 10*x2*x2 + 10*x3*x3 + 10*x4*x4 + 10*x5*x5 + 10*x6*x6 + 10*x7*x7) - 20*x1 - 80*x2 - 20*x3 - 50*x4 - 60*x5 - 90*x6) - 10*x8 - 10*x9 - 10*x10 + objvar =E= 0; e2.. - 2*x1 - 6*x2 - x3 - 3*x5 - 3*x6 - 2*x7 - 6*x8 - 2*x9 - 2*x10 =L= -4; e3.. 6*x1 - 5*x2 + 8*x3 - 3*x4 + x6 + 3*x7 + 8*x8 + 9*x9 - 3*x10 =L= 22; e4.. - 5*x1 + 6*x2 + 5*x3 + 3*x4 + 8*x5 - 8*x6 + 9*x7 + 2*x8 - 9*x10 =L= -6; e5.. 9*x1 + 5*x2 - 9*x4 + x5 - 8*x6 + 3*x7 - 9*x8 - 9*x9 - 3*x10 =L= -23; e6.. - 8*x1 + 7*x2 - 4*x3 - 5*x4 - 9*x5 + x6 - 7*x7 - x8 + 3*x9 - 2*x10 =L= -12; e7.. - 7*x1 - 5*x2 - 2*x3 - 6*x5 - 6*x6 - 7*x7 - 6*x8 + 7*x9 + 7*x10 =L= -3; e8.. x1 - 3*x2 - 3*x3 - 4*x4 - x5 - 4*x7 + x8 + 6*x9 =L= 1; e9.. x1 - 2*x2 + 6*x3 + 9*x4 - 7*x6 + 9*x7 - 9*x8 - 6*x9 + 4*x10 =L= 12; e10.. - 4*x1 + 6*x2 + 7*x3 + 2*x4 + 2*x5 + 6*x7 + 6*x8 - 7*x9 + 4*x10 =L= 15; e11.. x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 =L= 9; e12.. - x1 - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 =L= -1; * set non-default bounds x1.up = 1; x2.up = 1; x3.up = 1; x4.up = 1; x5.up = 1; x6.up = 1; x7.up = 1; x8.up = 1; x9.up = 1; x10.up = 1; * set non-default levels x1.l = 1; x2.l = 0.90755; x4.l = 1; x5.l = 0.71509; x6.l = 1; x8.l = 0.91698; x9.l = 1; x10.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 NLP $set NLP NLP Solve m using %NLP% minimizing objvar;
Last updated: 2024-11-25 Git hash: de62f3e5