What does this research mean for the field?

Necessary optimality conditions for nonlinear inverse problems governed by evolutionary quasi-hemivariational inequalities with parameter-dependent constraints can be derived using a double-approximation strategy combining smoothing and penalization. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Analyze nonlinear inverse problems governed by evolutionary quasi-hemivariational inequalities featuring parameter-dependent constraints to establish well-posedness and necessary optimality conditions.

September 14, 2026Nonlinear Analysis Real World ApplicationsOpen Access

Existence and necessary optimality conditions for nonlinear inverse problems governed by quasi-hemivariational inequalities with parameter-dependent constraints

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Authors

NANguyễn Thị Vân AnhVinh University AKAkhtar A. KhanRochester Institute of Technology VLVy Khoi LeMissouri University of Science and Technology

Discussion

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Implication

Theoretical analysis demonstrates existence and necessary optimality conditions in evolutionary quasi-hemivariational inequalities, highlighting solvable frameworks for complex inverse problems.

Key Points

Analyze nonlinear inverse problems governed by evolutionary quasi-hemivariational inequalities featuring parameter-dependent constraints to establish well-posedness and necessary optimality conditions.
Formulated the parametric forward problem within evolution triples to establish existence, uniqueness, and a priori estimates for the state system.
Framed the inverse problem as a Tikhonov-regularized output-least-squares optimization problem resolved through the direct method of the calculus of variations.
Employed a double-approximation strategy coupling smoothing and penalization techniques to address nonsmoothness and state constraints with potentially empty interiors.
Proved the existence of at least one optimal parameter for the regularized inverse problem.
Derived an adjoint system and a first-order variational inequality associated with a singular Lagrange multiplier to characterize necessary optimality.
Demonstrated the framework's applicability on a nonlinear parabolic quasi-obstacle problem formulated in Sobolev spaces, successfully yielding explicit optimality conditions.

Cite This Study

Anh et al. (2026) studied this question.

synapsesocial.com/papers/6aa7b3ee0926e14a848b33dd https://doi.org/10.1016/j.nonrwa.2026.104753

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Implication

Theoretical analysis demonstrates existence and necessary optimality conditions in evolutionary quasi-hemivariational inequalities, highlighting solvable frameworks for complex inverse problems.