More test examples for nonlinear programming codes
More test examples for nonlinear programming codes
Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Asymptotic admissibility of the unit stepsize in exact penalty functions
SIAM Journal on Control and Optimization
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Mathematical Programming: Series A and B
An analysis of reduced Hessian methods for constrained optimization
Mathematical Programming: Series A and B
Partitioned quasi-Newton methods for nonlinear equality constrained optimization
Mathematical Programming: Series A and B
Sizing and least-change secant methods
SIAM Journal on Numerical Analysis
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
Practical Update Criteria for Reduced Hessian SQP: Global Analysis
SIAM Journal on Optimization
SIAM Journal on Optimization
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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A technique for maintaining the positive definiteness of the matrices in the quasi-Newton version of the SQP algorithm is proposed. In our algorithm, matrices approximating the Hessian of the augmented Lagrangian are updated. The positive definiteness of these matrices in the space tangent to the constraint manifold is ensured by a so-called piecewise line-search technique, while their positive definiteness in a complementary subspace is obtained by setting the augmentation parameter. In our experiment, the combination of these two ideas leads to a new algorithm that turns out to be more robust and often improves the results obtained with other approaches.