Definable nonconvex parametric optimization problems admit an adjoint state formula under a qualification condition, selecting a conservative field for the value function without smoothness or uniqueness assumptions.
Springer, 1998
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Any maximally monotone operator can be approximated in local graph convergence by continuous encoder-decoder networks, with structure-preserving versions that retain maximal monotonicity via resolvent parameterizations.
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The adjoint state method for parametric definable optimization without smoothness or uniqueness
Definable nonconvex parametric optimization problems admit an adjoint state formula under a qualification condition, selecting a conservative field for the value function without smoothness or uniqueness assumptions.
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Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
Any maximally monotone operator can be approximated in local graph convergence by continuous encoder-decoder networks, with structure-preserving versions that retain maximal monotonicity via resolvent parameterizations.