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.
Constraint qualifications and lagrange multipliers in nondifferentiable programming problems.Journal of Optimization Theory and Applications, 81(3): 533–548, 1994
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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.