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TOMLAB /SPRNLP
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TOMLAB /BARNLP and TOMLAB /SRPNLP are the key computational packages in the TOMLAB /SOCS package. The solvers are fully integrated with the TOMLAB /SOCS package, however the solvers can be acquired separately and used for any supported problem type.
The TOMLAB /SPRNLP solver is a state-of-the-art sequential quadratic programming method, SQP, using an augmented Lagrangian merit function and safeguarded line search. The solver supports nonlinear equality and inequality constraints and simple bounds.
The TOMLAB /BARNLP solver implements a sparse primal-dual interior point algorithm, in conjunction with a filter method for globalization.
Features and capabilities
The solver package supports six different levels of functionality:
| Sparse NLP |
Provides general-purpose constrained optimization capability for very large applications. Unique features include:
- Sparse Quadratic Programming - Schur-Complement QP Method needs only one sparse matrix factorization, even with active set changes.
- Primal-Dual interior point method efficient even with many inequality constraints.
- Sparse Linear Algebra - Multifrontal solution of symmetric indefinite systems with pivoting for stability, using award-winning 1 Boeing software BCSLIB-EXT.
- Arbitrary Jacobian and Hessian Sparsity - Not restricted to block diagonal or other special form.
- Quadratic Convergence - Efficient solution for very large problems. The solver package can solve problem with roughly 500,000 variables and 500,000 constraints.
- No Restriction on Degrees of Freedom. Unlike reduced Hessian methods, SPRNLP and BARNLP converge efficiently when the final active set is small or large.
- Reverse Communication Format - Permits analytic and/or finite difference gradients.
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| Sparse Least Squares |
Provides nonlinearly constrained least squares capability with all of the features of the general sparse NLP. Unique features include:
- Numerically Stable Solution - Augmented QP format avoids formation of the normal matrix.
- Linear Least Squares - Special option for linearly constrained (e.g., data fitting) applications.
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| Dense NLP - Simplified usage |
Provides general-purpose constrained optimization capability for small- to moderate-size applications with limited user requirements. Its features include:
- User Supplies Functions - SPRNLP or BARNLP does the rest.
- Hessian Options - Quasi-Newton (SR1, BFGS, SSQN) and finite difference Newton.
- Finite Difference Jacobian/gradient.
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| Dense NLP - Sophisticated Usage |
| Provides general-purpose constrained optimization capability for small- to moderate-size applications with more complex interface requirements. In addition to capabilities of the simplified usage version, it uses a Reverse Communication Format that permits the user to supply Jacobian and optionally Hessian information. |
| Sparse Finite Difference Derivatives |
In addition to the optimization tools, this package provides a collection of tools for computing first and second derivatives (Jacobian and Hessian) for sparse matrices. Unique features include:
- Number of perturbations much smaller than number of variables!
- Jacobian/Hessian Evaluation - These procedures compute first and second derivative information using sparse differences.
- Index Set Construction - Given matrix sparsity, this procedure determines how to group the variables for efficient differentiation.
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| Minimum Curvature Data Approximation |
Multivariate tabular data can be approximated using tensor product spline functions. The software computes spline coefficients to:
- Minimize the curvature.
- Interpolate and/or approximate table data.
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Requirements
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