The use of slack variables in the adjoint method applied to tumor drug dosage

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Abstract

In this article, a novel approach for solving optimal control problems with inequality constraints is presented using a modified gradient method based on the adjoint technique. So far, the incorporation of inequality constraints in the adjoint approach requires the introduction of additional penalty terms in the cost function. However, such an approach may lead to a potential distortion of optimal control due to the need for weighting factors for these terms. The method proposed in this article avoids the use of penalty functions and allows the iterative computation of optimal controls. In order to demonstrate the effectiveness of the method, the algorithm is applied to the optimization problem of anti-angiogenesis of tumors in medicine. Tumor growth is closely related to the formation of new blood vessels. Above a certain tumor size, tumors expand their vascular network, a process known as angiogenesis. Targeting this process with anti-angiogenic therapy holds great promise for cancer treatment. Mathematical modeling and the use of optimal control theory enables the understanding of tumor dynamics and optimize treatment strategies. In this article this mathematical model for computing an optimal treatment therapy is considered. For this purpose, an adjoint gradient approach will be exploited in this article, to solve the optimal control problem iteratively by an optimization algorithm.
Original languageEnglish (American)
Title of host publicationProceedings of the ASME 2024, International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC2024, August 25-28, 2024
Place of PublicationPortland, USA
Number of pages2
Publication statusPublished - 2024
EventInternational Design Engineering Technical Conferences & Computers and Information in Engineering Conference - Washington, United States
Duration: 25 Aug 202428 Aug 2024

Conference

ConferenceInternational Design Engineering Technical Conferences & Computers and Information in Engineering Conference
Abbreviated titleIDETC2024
Country/TerritoryUnited States
CityWashington
Period25.08.202428.08.2024

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