Extend constraint dissolving mappings to general set-membership constraints

Resolve the technical challenges caused by the nondifferentiability of the projection operator $P_C(G(x))$ in order to construct and analyze constraint dissolving mappings for general set-membership constraints $G(x)\in C$, rather than restricting the framework to equality constraints with $C:=\{0\}$.

Background

The proposed constraint dissolving framework is formulated for optimization problems with general set-membership constraints $G(x)\in C$, where $C$ is a closed convex set, and geometric constraints $x\in D$, where $D$ may be nonconvex. However, the explicit construction of the constraint dissolving mapping relies on the projection $P_C(G(x))$.

Because this projection can be nondifferentiable in the general set-membership setting, the paper’s concrete construction and numerical analysis are restricted to equality constraints, corresponding to $C:=\{0\}$. Extending the construction to general closed convex sets would broaden the applicability of the method beyond the equality-constrained cases treated in the implementation section.