MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance st_qpk1
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | -3.00000000 (ANTIGONE) -3.00000000 (BARON) -3.00000000 (COUENNE) -3.00000000 (CPLEX) -3.00000096 (GUROBI) -3.00000000 (LINDO) -3.00000000 (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. Shectman, J P, Finite Algorithms for Global Optimization of Concave Programs and General Quadratic Programs, PhD thesis, Department of Mechanical and Industrial Engineering, University of Illinois, Urbana Champagne, 1999. |
Sourceⓘ | BARON book instance iqp/qpk1 |
Added to libraryⓘ | 03 Sep 2002 |
Problem typeⓘ | QP |
#Variablesⓘ | 2 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 2 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 0 |
Objective Senseⓘ | min |
Objective typeⓘ | quadratic |
Objective curvatureⓘ | concave |
#Nonzeros in Objectiveⓘ | 2 |
#Nonlinear Nonzeros in Objectiveⓘ | 2 |
#Constraintsⓘ | 4 |
#Linear Constraintsⓘ | 4 |
#Quadratic Constraintsⓘ | 0 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | linear |
#Nonzeros in Jacobianⓘ | 8 |
#Nonlinear Nonzeros in Jacobianⓘ | 0 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 4 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 2 |
#Blocks in Hessian of Lagrangianⓘ | 1 |
Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 1.0000e+00 |
Maximal coefficientⓘ | 3.0000e+00 |
Infeasibility of initial pointⓘ | 0 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 5 1 0 4 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 3 3 0 0 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 11 9 2 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,objvar; Positive Variables x1,x2; Equations e1,e2,e3,e4,e5; e1.. - x1 + x2 =L= 1; e2.. x1 - x2 =L= 1; e3.. - x1 + 2*x2 =L= 3; e4.. 2*x1 - x2 =L= 3; e5.. -(2*x1 - 2*x1*x1 + 2*x1*x2 + 3*x2 - 2*x2*x2) + objvar =E= 0; 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