An SQP Augmented Lagrangian BFGS Algorithm for Constrained Optimization
Byrd, Richard H.
In this research we present an effective algorithm for nonlinearly constrained optimization using the structured augmented Lagrangian secant update recently proposed by Tapia. The algorithm is globally defined, and uses a new and reliable method for choosing the Lagrangian augmentation parameter that does not require prior knowledge of the true Hessian. We present considerable numerical experimentation with this algorithm, both embedded in a merit-function line search SQP framework, and without line search.We compare the algorithm to the widely-used damped BFGS secant update of Powell, which, like ours, was designed to circumvent the lack of positive definiteness in the Hessian of the Lagrangian. We also establish the powerful and surprising convergence rate result, that when our algorithm converges it converges R-superlinearly. An immediate corollary is a new result in unconstrained optimization: whenever the unconstrained BFGS secant method converges, it does so Q-superlinearly. Our study has led us to the conclusion that when properly implemented Tapia's structured augmented Lagrangian BFGS secant update offers significant theoretical and tangible numerical advantages over Powell's damped BFGS update.
Citable link to this pagehttps://hdl.handle.net/1911/101656
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