Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 321–338
Convex Reformulation and Hybrid Optimization for Diabetes Treatment Planning: A Scalable Framework
Wahlaa Abbas Ajel Al-Basher, Azal Jaafar Musa Mera and Ahmed Sabah Ahmed Al-Jilawi
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Abstract
Diabetes mellitus is a disease affecting 460 million people globally, costing more than $966 billion annually. Thus, there is a need for personalization in diabetes management. This paper proposes a novel method for reformulating the traditionally intractable mixed-integer nonlinear programming (MINLP) problem into a polynomial-time solvable convex quadratic program (QP). We develop five optimization algorithms for solving the problem: Interior Point Method, Alternating Direction Method of Multipliers (ADMM), Proximal Gradient Method, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), Cutting Plane Method, and a novel four-stage algorithm called Hybrid. These algorithms are guaranteed to converge based on our curvature analysis. The curvature analysis shows strict concavity due to constant negative Hessian eigenvalues (λ_1=-20,λ_2=-15), excellent conditioning (κ=5), and strong convexity (μ=15), guaranteeing global optimality and rapid convergence. Our experiments conducted on 50 patients with 10 interventions (750 features) show better results than existing methods. The objective value is -182.48 with the proposed Hybrid algorithm compared with the value of -158.68 with the ADMM algorithm (15%) improvement. The violation in the feasible region is 10^(-4) with the proposed algorithm compared with the 10^(-2) ADMM algorithm (100-fold enhancement). Computational time remains competitive at 42 seconds. This framework extends to other chronic disease management problems. Providing both rigorous mathematical foundations and algorithms for population-scale healthcare optimization with guaranteed global optimality.
Keywords
Convex Optimization Curvature Analysis Diabetes Treatment Planning Healthcare Operations Research Hybrid Algorithm Personalized Medicine
References
  1. K. Fujihara and H. Sone, “Machine learning approach to drug treatment strategy for diabetes care,” Diabetes Metab. J., vol. 47, no. 3, pp. 325-332, 2023, [Online]. Available: https://doi.org/10.4093/dmj.2022.0349.
  2. A. Tuppad and S. D. Patil, “Machine learning for diabetes clinical decision support: a review,” Adv. Comp. Int., vol. 2, p. 22, 2022, [Online]. Available: https://doi.org/10.1007/s43674-022-00034-y.
  3. N. A. ElSayed et al., “Summary of revisions: standards of care in diabetes-2023,” Diabetes Care, vol. 46, no. Supplement_1, pp. S5-S9, 2023, [Online]. Available: https://doi.org/10.2337/dc23-Srev.
  4. N. A. ElSayed et al., “Summary of revisions: standards of care in diabetes-2024,” Diabetes Care, vol. 47, no. Supplement_1, pp. S5-S10, 2024, [Online]. Available: https://doi.org/10.2337/dc24-SREV.
  5. M. J. Davies et al., “Management of hyperglycaemia in type 2 diabetes, 2022. A consensus report by the American Diabetes Association (ADA) and the European Association for the Study of Diabetes (EASD),” Diabetologia, vol. 65, pp. 1925-1966, 2022, [Online]. Available: https://doi.org/10.1007/s00125-022-05787-2.
  6. D. M. Nathan et al., “Medical management of hyperglycemia in type 2 diabetes: a consensus algorithm for the initiation and adjustment of therapy: a consensus statement of the American Diabetes Association and the European Association for the Study of Diabetes,” Clin. Diabetes, vol. 27, no. 1, pp. 4-16, 2009, [Online]. Available: https://doi.org/10.2337/diaclin.27.1.4.
  7. S. E. Inzucchi et al., “Management of hyperglycemia in type 2 diabetes, 2015: a patient-centered approach: update to a position statement of the American Diabetes Association and the European Association for the Study of Diabetes,” Diabetes Care, vol. 38, no. 1, pp. 140-149, 2015, [Online]. Available: https://doi.org/10.2337/dc14-2441.
  8. E. K. Lee, X. Wei, M. D. Wright, and F. Baker-Witt, “A Personalized Dosing Strategy Optimization for Diabetes Management: Applications to Gestational Diabetes Mellitus,” AMIA Annu. Symp. Proc., vol. 2024, pp. 638-647, 2024.
  9. S. Griffin, K. Claxton, N. Hawkins, and M. Sculpher, “Probabilistic analysis and computationally expensive models: necessary and required?,” Value Health, vol. 9, no. 4, pp. 244-252, 2006, [Online]. Available: https://doi.org/10.1111/j.1524-4733.2006.00107.x.
  10. A. J. Palmer et al., “The CORE Diabetes Model: projecting long-term clinical outcomes, costs and cost-effectiveness of interventions in diabetes mellitus (types 1 and 2) to support clinical and reimbursement decision-making,” Curr. Med. Res. Opin., vol. 20, no. sup1, pp. S5-S26, 2004, [Online]. Available: https://doi.org/10.1185/030079904X1980.
  11. M. Komorowski, L. A. Celi, O. Badawi, A. C. Gordon, and A. A. Faisal, “The artificial intelligence clinician learns optimal treatment strategies for sepsis in intensive care,” Nat. Med., vol. 24, pp. 1716-1720, 2018, [Online]. Available: https://doi.org/10.1038/s41591-018-0213-5.
  12. N. Razavian, J. Marcus, and D. Sontag, “Multi-task prediction of disease onsets from longitudinal laboratory tests,” in Machine Learning for Healthcare Conference, 2016, pp. 73-100.
  13. N. Karmarkar, “A new polynomial-time algorithm for linear programming,” in Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing, 1984, pp. 302-311, [Online]. Available: https://doi.org/10.1145/800057.808695.
  14. S. Mehrotra, “On the implementation of a primal-dual interior point method,” SIAM J. Optim., vol. 2, no. 4, pp. 575-601, 1992, [Online]. Available: https://doi.org/10.1137/0802028.
  15. Y. Nesterov and A. Nemirovskii, Interior-Point Polynomial Algorithms in Convex Programming. Philadelphia, PA, USA: SIAM, 1994.
  16. R. Glowinski and A. Marroco, “On the approximation, by first-order finite elements, and the solution, by penalization-duality, of a class of nonlinear Dirichlet problems,” Rev. Fr. Autom., Inf. Rech. Oper., Ser.: Anal. Numer., vol. 9, no. R2, pp. 41-76, 1975.
  17. P. Neal, C. Eric, P. Borja, and E. Jonathan, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1-122, 2011, [Online]. Available: https://doi.org/10.1561/2200000016.
  18. J. Eckstein and D. P. Bertsekas, “On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators,” Math. Program., vol. 55, pp. 293-318, 1992, [Online]. Available: https://doi.org/10.1007/BF01581204.
  19. Y. Nesterov, “A method for solving the convex programming problem with convergence rate O(1/k²),” Rep. Acad. Sci., vol. 269, p. 543, 1983.
  20. A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci., vol. 2, no. 1, pp. 183-202, 2009, [Online]. Available: https://doi.org/10.1137/080716542.
  21. J. E. Kelley, “The cutting-plane method for solving convex programs,” J. Soc. Ind. Appl. Math., vol. 8, no. 4, pp. 703-712, 1960, [Online]. Available: https://doi.org/10.1137/0108053.
  22. S. Elhedhli, “Exact solution of a class of nonlinear knapsack problems,” Oper. Res. Lett., vol. 33, no. 6, pp. 615-624, 2005, [Online]. Available: https://doi.org/10.1016/j.orl.2005.01.004.
  23. H. Pirkul and V. Jayaraman, “A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution,” Comput. Oper. Res., vol. 25, no. 10, pp. 869-878, 1998, [Online]. Available: https://doi.org/10.1016/S0305-0548(97)00096-8.
  24. Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí, “Scatter search and local NLP solvers: A multistart framework for global optimization,” INFORMS J. Comput., vol. 19, no. 3, pp. 328-340, 2007, [Online]. Available: https://doi.org/10.1287/ijoc.1060.0175.
  25. Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course. Dordrecht, Netherlands: Kluwer Academic Publishers, 2004.
  26. J. Nocedal and S. J. Wright, Numerical Optimization. New York, NY, USA: Springer, 2006.
  27. J. Gondzio, “Interior point methods 25 years later,” Eur. J. Oper. Res., vol. 218, no. 3, pp. 587-601, 2012, [Online]. Available: https://doi.org/10.1016/j.ejor.2011.09.017.
  28. L. A. Wolsey, Integer Programming. New York, NY, USA: John Wiley & Sons, 1998.
  29. B. He and X. Yuan, “On the O(1/n) convergence rate of the Douglas-Rachford alternating direction method,” SIAM J. Numer. Anal., vol. 50, no. 2, pp. 700-709, 2012, [Online]. Available: https://doi.org/10.1137/110836936.

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