G-2025-33
Solving slgorithm NCL's subproblems: The need for interior methods
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Algorithm NCL was devised to solve a class of large
nonlinearly constrained optimization problems whose constraints do
not satisfy LICQ at a solution. It is mathematically equivalent to
the augmented Lagrangian algorithm LANCELOT, which solves a short
sequence of bound-constrained subproblems BCk
and has no LICQ
difficulties. NCL's equivalent subproblems NCk
are much bigger
and must be solved by a nonlinear interior method (needing
first and second derivatives). We study the KKT-type systems arising
within nonlinear interior methods when they are applied to the NCk
subproblems. We find that the KKT systems can sometimes
be reduced to smaller SQD systems (symmetric quasi-definite)
and sometimes to even smaller SPD systems (symmetric positive definite).
The smaller systems have proved suitable for GPU implementation within the interior solver MadNLP when it used by MadNCL to implement Algorithm NCL.
Paru en avril 2025 , 4 pages
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