MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance quantum

Find energy eigenvalues of the anharmonic oscillator with g=1 in the Gaussian and Post-Gaussian variational methods.
Formats ams gms osil
Primal Bounds (infeas ≤ 1e-08)
0.80490293 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds  
References Ogura, Akihiro, Post-Gaussian variational method for quantum anharmonic oscillator, Tech. Rep. arXiv:physics/9905056v1, Laboratory of Physics, College of Science and Technology, Nihon University, 1999.
Source GAMS Model Library model quantum
Application Quantum Mechanics
Added to library 18 Aug 2014
Problem type NLP
#Variables 2
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 2
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature unknown
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 2
#Constraints 0
#Linear Constraints 0
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions div gamma mul rpower sqr
Constraints curvature linear
#Nonzeros in Jacobian 0
#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 5.0000e-01
Maximal coefficient 2.5000e+00
Infeasibility of initial point 0
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          1        1        0        0        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
*          3        1        2        0
*
*  Solve m using DNLP minimizing objvar;


Variables  objvar,x2,x3;

Equations  e1;


e1.. -(0.5*sqr(x3)*Gamma(2 - 0.5/x3)/Gamma(0.5/x3)*x2**(1/x3) + 0.5*Gamma(1.5/
     x3)/Gamma(0.5/x3)*x2**(-1/x3) + Gamma(2.5/x3)/Gamma(0.5/x3)*x2**(-2/x3))
      + objvar =E= 0;

* set non-default bounds
x2.lo = 0.0001; x2.up = 10;
x3.lo = 0.001; x3.up = 10;

* set non-default levels
x2.l = 1;
x3.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 DNLP $set DNLP DNLP
Solve m using %DNLP% minimizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
Imprint / Privacy Policy / License: CC-BY 4.0