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Nonlinear Constrained Optimization

The online software section has been disabled indefinitely due to server usage policies. Please check back here at a later date.

The following is a web implementation of the Sequential Quadratic Programming algorithm implemented in VMCON2 to minimize a nonlinear function subject to nonlinear constraints. The general nonlinear constrained optimization problem can be stated as

Min { f(x) : g(x) <= 0, h(x) = 0 }

where x is the vector of optimization variables, f(x) is the objective function to be minimized, g(x) is the vector of inequality constraints, and h(x) is the vector of equality constraints. Simple bounds on x can be included as inequality constraints.

VMCON2 allows finite difference approximation of gradients when analytical derivatives are not available. The routine uses Powell's SQP algorithm, which contains two major steps per iteration:

  • Solve a positive definite quadratic programming (QP) subproblem to determine a search direction. The QP objective function is obtained by linearizing the Lagrangian function, while the QP constraints are obtained by linearizing the constraints g and h.
  • Apply a one-dimensional search along the direction obtained above for a function which is a linear combination of the objective function and those constraints which are not satisfied

Input Data

Browse or specify the path of the file containing the FORTRAN code for the objective function to be minimized. The format of this file is available here.

  • Path of file containing the objective function : or

  • Choose objective function example :

Browse or specify the path of file containing the FORTRAN code for the equality (first) and inequality constraints (in negative null form). A description of the file formats is available here.
  • Path of file containing the constraints : or

Specify the number of variables, equality constraints, inequality constraints, and the termination criterion. The default values are for the provided example.

  • Number of variables:
  • Number of equality constraints:
  • Number of inequality constraints:

Browse or specify the path of file containing the initial point. The format of this file is available here.

  • Path of file containing the initial point : or

  • Choose initial point for the example :

Browse or specify the path of file containing the source code of FORTRAN subroutines and functions called by the code uploaded above.
  • Path of file containing other FORTRAN subroutines and functions : or

  • No file to upload :

Acknowledgements

This site is supported by the Automotive Research Center at the University of Michigan, a US Army TACOM Center of Excellence for Modeling and Simulation of Ground Vehicles, under Contract No. DAAE07-94-R094.

Web Development Team

Chung-Han (Joe) Lin, Web Specialist

Dr. Nestor Michelena, Web Project Leader

Reference

  • R.C. Crane, K.E. Hillstrom, and M. Minkoff, Solution of the General Nonlinear Programming Problem with Subroutine VMCON
 
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