A Convex Bi-Level Optimization Model for Health Information Governance and Management: Karush{Kuhn{Tucker Reformulation and Existence Results
DOI:
https://doi.org/10.26713/cma.v17i3.3589Keywords:
Bi-level optimization, health information governanceAbstract
Health Information Governance (HIG) and Health Information Management (HIM) are structurally distinct components of regulated information systems, yet their hierarchical interaction has not been formalized within a rigorous optimization framework. We formulate this interaction as a convex bi-level optimization problem in which governance selects policy parameters defining the admissible operational region, while management solves a convex quadratic program subject to governance-induced constraints.
Under convexity and Slater-type regularity assumptions, we establish equivalence between the bi-level formulation and a single-level mathematical program with equilibrium constraints obtained via Karush--Kuhn--Tucker reformulation. We prove existence of optimal solutions under compactness and boundedness conditions and derive structural monotonicity properties showing that policy tightening induces contraction of the lower-level feasible set. These results provide a precise mathematical characterization of governance as a constraint-generating upper layer distinct from operational optimization. A stylized healthcare case study illustrates the resulting trade-off between compliance strictness and operational efficiency.
The framework provides a mathematically rigorous approach to hierarchical policy-constrained optimization in regulated information systems.
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bibitem{adil2022}
M. A. Khan, H. Ullah, T. Saeed, H. H. Alsulami, Z. M. M. Sayed and A. M. Alshehri,
Estimations of the Slater gap via convexity and its applications in information theory,
textit{Mathematical Problems in Engineering}, 2022 (2022), Article ID 1750331.
bibitem{adil2024}
M. A. Khan, H. Ullah, T. Saeed, Z. M. M. Sayed, S. Alshaikey and E. E. Mahmoud,
Determination of novel estimations for the Slater difference and applications,
textit{Complexity}, 2024 (2024), Article ID 8481103.
bibitem{anandalingam1992}
G. Anandalingam and T. L. Friesz,
Hierarchical optimization: An introduction,
textit{Annals of Operations Research}, 34 (1992), 1--11.
bibitem{amer2017}
A. H. Amer,
On the Karush--Kuhn--Tucker reformulation of bi-level geometric programming problem with interval coefficients as multiple parameters,
textit{Journal of Progressive Research in Mathematics}, 11 (2017), 1566--1577.
bibitem{arrow1958}
K. J. Arrow, L. Hurwicz and H. Uzawa,
textit{Studies in Linear and Non-Linear Programming},
Stanford University Press, Stanford, 1958.
bibitem{bard1999}
J. F. Bard,
textit{Practical Bilevel Optimization: Algorithms and Applications},
Springer, New York, 1999.
bibitem{ben2001}
A. Ben-Tal and A. Nemirovski,
textit{Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications},
SIAM, Philadelphia, 2001.
bibitem{bertsekas1997}
D. P. Bertsekas,
Nonlinear programming,
textit{Journal of the Operational Research Society}, 48 (1997), 334.
bibitem{boyd2004}
S. Boyd and L. Vandenberghe,
textit{Convex Optimization},
Cambridge University Press, Cambridge, 2004.
bibitem{brandeau2004}
M. L. Brandeau, F. Sainfort and W. P. Pierskalla (eds.),
textit{Operations Research and Health Care: A Handbook of Methods and Applications},
Springer, New York, 2004.
bibitem{cardoen2010}
B. Cardoen, E. Demeulemeester and J. Beliën,
Operating room planning and scheduling: A literature review,
textit{European Journal of Operational Research}, 201 (2010), 921--932.
bibitem{colson2007}
B. Colson, P. Marcotte and G. Savard,
An overview of bilevel optimization,
textit{Annals of Operations Research}, 153 (2007), 235--256.
bibitem{dempe1993}
S. Dempe,
Directional differentiability of optimal solutions under Slater's condition,
textit{Mathematical Programming}, 59 (1993), 49--69.
bibitem{dempe2002}
S. Dempe,
textit{Foundations of Bilevel Programming},
Springer, Dordrecht, 2002.
bibitem{dempe2007}
S. Dempe, J. Dutta and B. S. Mordukhovich,
New necessary optimality conditions in optimistic bilevel programming,
textit{Optimization}, 56 (2007), 577--604.
bibitem{facchinei2003}
F. Facchinei and J.-S. Pang,
textit{Finite-Dimensional Variational Inequalities and Complementarity Problems},
Springer, New York, 2003.
bibitem{fenton2017}
S. H. Fenton, S. Low, K. J. Abrams and K. Butler-Henderson,
Health information management: Changing with time,
textit{Yearbook of Medical Informatics}, 26 (2017), 72--77.
bibitem{fletcher2013}
R. Fletcher,
textit{Practical Methods of Optimization},
John Wiley & Sons, Chichester, 2013.
bibitem{gaudioso2022}
M. Gaudioso, G. Giallombardo and G. Miglionico,
Essentials of numerical nonsmooth optimization,
textit{Annals of Operations Research}, 314 (2022), 213--253.
bibitem{gupta1992}
R. K. Gupta,
textit{Operations Research},
Krishna Prakashan Media, Meerut, 1992.
bibitem{kerr2003}
S. Kerr and R. G. Newell,
Policy-induced technology adoption: Evidence from the US lead phasedown,
textit{The Journal of Industrial Economics}, 51 (2003), 317--343.
bibitem{luo1996}
Z.-Q. Luo, J.-S. Pang and D. Ralph,
textit{Mathematical Programs with Equilibrium Constraints},
Cambridge University Press, Cambridge, 1996.
bibitem{nocedal2006}
J. Nocedal and S. J. Wright,
textit{Numerical Optimization},
Springer, New York, 2006.
bibitem{rockafellar1970}
R. T. Rockafellar,
textit{Convex Analysis},
Princeton University Press, Princeton, 1970.
bibitem{yang2013}
Z. Yang, A. Kankanhalli, B.-Y. Ng and J. T. Y. Lim,
Analyzing the enabling factors for the organizational decision to adopt healthcare information systems,
textit{Decision Support Systems}, 55 (2013), 764--776.
bibitem{ye1995}
J. J. Ye and D. L. Zhu,
Optimality conditions for bilevel programming problems,
textit{Optimization}, 33 (1995), 9--27.
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