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- W1972504036 abstract "In this article we propose a new approach to constrained optimization that is based on direct and adjoint vector-function evaluations in combination with secant updating. The main goal is the avoidance of constraint Jacobian evaluations and the reduction of the linear algebra cost per iteration to $ {cal O}(n + m)^2 $ operations in the dense, unstructured case. A crucial building block is a transformation invariant two-sided-rank-one update (TR1) for approximations to the (active) constraint Jacobian. In this article we elaborate its basic properties and report preliminary numerical results for the new total quasi-Newton approach on some small equality constrained problems. A nullspace implementation under development is briefly described. The tasks of identifying active constraints, safeguarding convergence and many other important issues in constrained optimization are not addressed in detail." @default.
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- W1972504036 date "2002-01-01" @default.
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- W1972504036 title "On constrained optimization by adjoint based quasi-Newton methods" @default.
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- W1972504036 doi "https://doi.org/10.1080/1055678021000060829" @default.
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