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Solving Singular Control Problems in Mathematical Biology, Using PASA

November 18 @ 1:00 pm - 2:00 pm KST

B378 Seminar room, IBS, 55 Expo-ro Yuseong-gu
Daejeon, 34126 Korea, Republic of
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Speaker

Aurelio A. de los Reyes V
IBS Biomedical Mathematics Group

We will discuss about “Solving Singular Control Problems in Mathematical Biology, Using PASA”, Atkins et al., arXiv, 2020

In this paper, we will demonstrate how to use a nonlinear polyhedral constrained optimization solver called the Polyhedral Active Set Algorithm (PASA) for solving a general singular control problem. We present methods of discretizing a general optimal control problem that involves the use of the gradient of the Lagrangian for computing the gradient of the cost functional so that PASA can be applied. When a numerical solution contains artifacts that resemble “chattering”, a phenomenon where the control oscillates wildly along the singular region, we recommend a method of regularizing the singular control problem by adding a term to the cost functional that measures a scalar multiple of the total variation of the control, where the scalar is viewed as a tuning parameter. We then demonstrate PASA’s performance on three singular control problems that give rise to different applications of mathematical biology. We also provide some exposition on the heuristics that we use in determining an appropriate size for the tuning parameter.

Details

Date:
November 18
Time:
1:00 pm - 2:00 pm KST
Event Category:

Organizer

Jae Kyoung Kim
Email:
jaekkim@kaist.ac.kr

Venue

B378 Seminar room, IBS
55 Expo-ro Yuseong-gu
Daejeon, 34126 Korea, Republic of
+ Google Map
IBS 의생명수학그룹 Biomedical Mathematics Group
기초과학연구원 수리및계산과학연구단 의생명수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Biomedical Mathematics Group (BIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
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