Least-change quasi-Newton updates for equality-constrained optimization | Zendy

Michael Wagner | Zendy; Michael J. Todd | Zendy

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Least-change quasi-Newton updates for equality-constrained optimization

Author(s) -

Michael Wagner,

Michael J. Todd

Publication year - 2000

Publication title -

mathematical programming

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.358

H-Index - 131

eISSN - 1436-4646

pISSN - 0025-5610

DOI - 10.1007/s101070050117

Subject(s) - hessian matrix , mathematics , convergence (economics) , rank (graph theory) , class (philosophy) , projection (relational algebra) , divergence (linguistics) , mathematical optimization , numerical analysis , quasi newton method , argument (complex analysis) , newton's method , mathematical analysis , combinatorics , computer science , nonlinear system , algorithm , linguistics , philosophy , physics , artificial intelligence , quantum mechanics , economics , economic growth , biochemistry , chemistry

. This paper investigates quasi-Newton updates for equality-constrained optimization. Using a least-change argument we derive a class of rank-3 updates to approximations of the one-sided projection of the Hessian of the Lagrangian which keeps the appropriate part symmetric (and possibly positive definite). By imposing the usual assumptions we are able to prove 1-step superlinear convergence for one of these updates. Encouraging numerical results and comparisons with other previously analyzed updates are presented.

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