## User's Guide For SNOPT 5.3: A Fortran Package For Large-Scale Nonlinear Programming (1999)

Citations: | 75 - 1 self |

### BibTeX

@TECHREPORT{Gill99user'sguide,

author = {Philip E. Gill and Walter Murray and Michael A. Saunders},

title = {User's Guide For SNOPT 5.3: A Fortran Package For Large-Scale Nonlinear Programming},

institution = {},

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

SNOPT is a general-purpose system for solving optimization problems involving many variables and constraints. 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 that obtains search directions from a sequence of quadratic programming subproblems. Each QP subproblem minimizes a quadratic model of a certain Lagrangian function subject to a linearization of the constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point. SNOPT is most efficient if only some of the variables enter nonlinearly, or if the number of active constraints (including simple bounds) is nearly as large as the number of variables. 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 for SNOPT is suitable for any machine with a Fortran compiler. SNOPT may be called from a driver program (typically in Fortran, C or MATLAB). SNOPT can also be used as a stand-alone package, reading data in the MPS ...

### Citations

809 |
Linear programming and extension
- Dantzig
(Show Context)
Citation Context ...ear and nonlinear functions. This structure can be exploited by SNOPT (see x3). If the nonlinear functions are absent, the problem is a linear program (LP) and SNOPT applies the primal simplex method =-=[2]-=-. Sparse basis factors are maintained by LUSOL [8] as in MINOS [13]. If only the objective is nonlinear, the problem is linearly constrained (LC) and tends to solve more easily than the general case w... |

328 | SNOPT: An SQP algorithm for Large-Scale Constrained Optimization
- Gill, Murray, et al.
- 2001
(Show Context)
Citation Context ...is linearly constrained (LC) and tends to solve more easily than the general case with nonlinear constraints (NC). For both cases, SNOPT applies a sparse sequential quadratic programming (SQP) method =-=[6]-=-, using limitedmemory quasi-Newton approximations to the Hessian of the Lagrangian. The merit function for steplength control is an augmented Lagrangian, as in the dense SQP solver NPSOL [7, 10]. In g... |

82 |
User’s guide for NPSOL (version 4.0): A Fortran package for nonlinear programming
- Gill, Murray, et al.
- 1986
(Show Context)
Citation Context ...P) method [6], using limitedmemory quasi-Newton approximations to the Hessian of the Lagrangian. The merit function for steplength control is an augmented Lagrangian, as in the dense SQP solver NPSOL =-=[7, 10]-=-. In general, SNOPT requires less matrix computation than NPSOL and fewer evaluations of the functions than the nonlinear algorithms in MINOS [11, 12]. It is suitable for nonlinear problems with thous... |

74 | Large-Scale Linearly Constrained Optimization
- Murtagh, Saunders
- 1978
(Show Context)
Citation Context ...ented Lagrangian, as in the dense SQP solver NPSOL [7, 10]. In general, SNOPT requires less matrix computation than NPSOL and fewer evaluations of the functions than the nonlinear algorithms in MINOS =-=[11, 12]-=-. It is suitable for nonlinear problems with thousands of constraints and variables, but not thousands of degrees of freedom. (Thus, for large problems there should be many constraints and bounds, and... |

26 |
An ℓ1 penalty method for nonlinear constraints
- Fletcher
- 1985
(Show Context)
Citation Context ...uivalent to minimizing the sum of the nonlinear constraint violations subject to the linear constraints and bounds. A similar ` 1 formulation of NP is fundamental to the S` 1 QP algorithm of Fletcher =-=[4]-=-. See also Conn [1]. 8 User's Guide for SNOPT 3. Identifying structure in the objective and constraints Consider the following nonlinear optimization problem with four variables x = (u; v; z; w): mini... |

20 |
Solving staircase linear programs by the simplex method, 1: Inversion
- Fourer
- 1982
(Show Context)
Citation Context ...y large elements (say, larger than 1000). 1 Linear constraints and variables are scaled by an iterative procedure that attempts to make the matrix coefficients as close as possible to 1.0 (see Fourer =-=[5]-=-). This will sometimes improve the performance of the solution procedures. 2 All constraints and variables are scaled by the iterative procedure. Also, an additional scaling is performed that takes in... |

15 |
Large-Scale Sequential Quadratic Programming Algorithms
- Eldersveld
- 1991
(Show Context)
Citation Context ...mum-norm perturbation that ensures descent for M [10]. As in NPSOL, s N is adjusted to minimize the merit function as a function of s prior to the solution of the QP subproblem. For more details, see =-=[7, 3]-=-. 2. Description of the method 7 2.5. Treatment of constraint infeasibilities SNOPT makes explicit allowance for infeasible constraints. Infeasible linear constraints are detected first by solving a p... |

13 |
Constrained optimization using a nondifferentiable penalty function, SIAMJournal on Numerical Analysis 10
- Conn
- 1973
(Show Context)
Citation Context ...ing the sum of the nonlinear constraint violations subject to the linear constraints and bounds. A similar ` 1 formulation of NP is fundamental to the S` 1 QP algorithm of Fletcher [4]. See also Conn =-=[1]-=-. 8 User's Guide for SNOPT 3. Identifying structure in the objective and constraints Consider the following nonlinear optimization problem with four variables x = (u; v; z; w): minimize (u + v + z) 2 ... |

4 |
5.5 User’s Guide
- MINOS
- 1998
(Show Context)
Citation Context ...OPT (see x3). If the nonlinear functions are absent, the problem is a linear program (LP) and SNOPT applies the primal simplex method [2]. Sparse basis factors are maintained by LUSOL [8] as in MINOS =-=[13]-=-. If only the objective is nonlinear, the problem is linearly constrained (LC) and tends to solve more easily than the general case with nonlinear constraints (NC). For both cases, SNOPT applies a spa... |