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Systems Optimization Laboratory

Stanford University
Dept of Management Science and Engineering (MS&E)

Huang Engineering Center

Stanford, CA 94305-4121  USA

User guide for SNOPT 7: Software for large-scale linear and quadratic programming

SNOPT is a general-purpose system for constrained optimization. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for large-scale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs.

SNOPT finds solutions that are locally optimal, and ideally any nonlinear functions should be smooth and users should provide gradients. It is often more widely useful. For example, local optima are often global solutions, and discontinuities in the function gradients can often be tolerated if they are not too close to an optimum. Unknown gradients are estimated by finite differences.

SNOPT uses a sequential quadratic programming (SQP) algorithm. Search directions are obtained from QP subproblems that minimize a quadratic model of the Lagrangian function subject to linearized constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point.

On large problems, SNOPT is most efficient if only some of the variables enter nonlinearly, or there are relatively few degrees of freedom at a solution (i.e., many constraints are active). SNOPT requires relatively few evaluations of the problem functions. Hence it is especially effective if the objective or constraint functions (and their gradients) are expensive to evaluate.

The source code is re-entrant and suitable for any machine with a Fortran 77, 90, or later compiler. We recommend gfortran (part of GCC, the GNU Compiler Collection). The f2c translation of the SNOPT f77 source code can be used with a C compiler. SNOPT may be called from a driver program in Fortran, C, or Matlab. It can also be used as a stand-alone package, reading data in the MPS format used by commercial mathematical programming systems.

See UCSD/Stanford Optimization Software for information about the solvers SNOPT, DNOPT, NPSOL, SQOPT, SQIC.

P. E. Gill, W. Murray, and M. A. Saunders (2008), SNOPT 7 User's Guide.

P. E. Gill, W. Murray, and M. A. Saunders (2005), SNOPT: An SQP algorithm for large-scale constrained optimization, SIAM Review 47(1), 99-131.