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\n\n \n \n \n \n \n Designing a Frank-Wolfe Algorithm for Simulation Optimization Over Unbounded Linearly Constrained Feasible Regions.\n \n \n \n\n\n \n Boonsiriphatthanajaroen, N.; and Henderson, S. G.\n\n\n \n\n\n\n In Azar, E.; Djanatliev, A.; Harper, A.; Kogler, C.; Ramamohan, V.; Anagnostou, A.; and Taylor, S. J. E., editor(s),
Proceedings of the 2025 Winter Simulation Conference, pages 3346-3357, Piscataway, New Jersey, 2025. IEEE\n
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@inproceedings{boohen25b,\n\tabstract = {The linearly constrained simulation optimization problem entails optimizing an objective function that is\nevaluated, approximately, through stochastic simulation, where the finite-dimensional decision variables\nlie in a feasible region defined by known, deterministic linear constraints. We assume the availability of\nunbiased gradient estimates. When the feasible region is bounded, existing algorithms are highly effective.\nWe attempt to extend existing algorithms to also allow for unbounded feasible regions. We extend both\nthe away-step (ASFW) and boosted Frank-Wolfe (BFW) algorithms. Computational experiments compare\nthese algorithms with projected gradient descent (PGD). An extension of BFW performs the best in our\nexperiments overall, performing substantially better than both PGD and ASFW. Moreover, PGD substantially\noutperforms ASFW. We provide commentary on our experimental results and suggest avenues for further\nalgorithm development. The article also showcases the use of the SimOpt Library (2025) in algorithm\ndevelopment. \n},\n\taddress = {Piscataway, New Jersey},\n\tauthor = {Natthawut Boonsiriphatthanajaroen and Shane G. Henderson},\n\tbooktitle = {Proceedings of the 2025 Winter Simulation Conference},\n\tdate-added = {2026-04-12 09:49:47 -0400},\n\tdate-modified = {2026-04-12 09:49:47 -0400},\n\teditor = {E. Azar and A. Djanatliev and A. Harper and C. Kogler and V. Ramamohan and A. Anagnostou and S. J. E. Taylor},\n\tpages = {3346-3357},\n\tpublisher = {IEEE},\n\ttitle = {Designing a Frank-Wolfe Algorithm for Simulation Optimization Over Unbounded Linearly Constrained Feasible Regions},\n\tyear = {2025}}\n\n\n
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\n The linearly constrained simulation optimization problem entails optimizing an objective function that is evaluated, approximately, through stochastic simulation, where the finite-dimensional decision variables lie in a feasible region defined by known, deterministic linear constraints. We assume the availability of unbiased gradient estimates. When the feasible region is bounded, existing algorithms are highly effective. We attempt to extend existing algorithms to also allow for unbounded feasible regions. We extend both the away-step (ASFW) and boosted Frank-Wolfe (BFW) algorithms. Computational experiments compare these algorithms with projected gradient descent (PGD). An extension of BFW performs the best in our experiments overall, performing substantially better than both PGD and ASFW. Moreover, PGD substantially outperforms ASFW. We provide commentary on our experimental results and suggest avenues for further algorithm development. The article also showcases the use of the SimOpt Library (2025) in algorithm development. \n
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\n\n \n \n \n \n \n Designing Interventions for Epidemics using Mathematical Programming: A Survey.\n \n \n \n\n\n \n Gande, V.; Kong, S.; Miller, C. J.; Xie, M.; Yu, G.; and Henderson, S. G.\n\n\n \n\n\n\n 2025.\n
Submitted.\n\n
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@unpublished{ganetal25,\n\tabstract = {We survey the design of interventions for epidemics using mathematical programming.\nWe do not attempt to survey control-theoretic approaches. The dominant areas of\napplication are in vaccine distribution, allocation and timing, and in other resource\nallocation problems such as the location and sizing of treatment centers and supply\nchain management for vaccines and other perishables. The dominant methodologies\nthat have been applied are mixed integer programming and nonlinear programming,\nthough many other operations research methodologies have seen use or exploration in\nthis context. We identify important lines of future work that center around 1) the\nintegration with statistical techniques for analyzing data; 2) parameter uncertainty in\nepidemic models; 3) the use of model hierarchies and 4) better capturing complex\nhuman behaviors.},\n\tauthor = {Varun Gande and Siyu Kong and Christian J. Miller and Miaolan Xie and George Yu and Shane G. Henderson},\n\tdate-added = {2025-11-25 16:24:12 -0500},\n\tdate-modified = {2025-11-25 16:26:35 -0500},\n\tnote = {Submitted.},\n\ttitle = {Designing Interventions for Epidemics using Mathematical Programming: A Survey},\n\tyear = {2025}}\n\n\n
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\n We survey the design of interventions for epidemics using mathematical programming. We do not attempt to survey control-theoretic approaches. The dominant areas of application are in vaccine distribution, allocation and timing, and in other resource allocation problems such as the location and sizing of treatment centers and supply chain management for vaccines and other perishables. The dominant methodologies that have been applied are mixed integer programming and nonlinear programming, though many other operations research methodologies have seen use or exploration in this context. We identify important lines of future work that center around 1) the integration with statistical techniques for analyzing data; 2) parameter uncertainty in epidemic models; 3) the use of model hierarchies and 4) better capturing complex human behaviors.\n
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\n\n \n \n \n \n \n \n Deterministic and Stochastic Frank-Wolfe Recursion on Probability Spaces.\n \n \n \n \n\n\n \n Yu, D.; Henderson, S. G.; and Pasupathy, R.\n\n\n \n\n\n\n
Mathematics of Operations Research. 2025.\n
To appear\n\n
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@article{yuhenpas24,\n\tabstract = {Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces, made especially possible by a lemma that identifies a ``closed-form'' solution to the infinite-dimensional Frank-Wolfe sub-problem. Each iterate in dFW is expressed as a convex combination of the incumbent iterate and a Dirac measure concentrating on the minimum of the influence function at the incumbent iterate. To address common application contexts that have access only to Monte Carlo observations of the objective and influence function, we construct a stochastic Frank-Wolfe (sFW) variation that generates a random sequence of probability measures constructed using minima of increasingly accurate estimates of the influence function. We demonstrate that sFW's optimality gap sequence exhibits O(1/k) iteration complexity almost surely and in expectation for smooth convex objectives, and O(1/sqrt(k)) (in Frank-Wolfe gap) for smooth non-convex objectives. Furthermore, we show that an easy-to-implement fixed-step, fixed-sample version of (sFW) exhibits exponential convergence to epsilon-optimality. We end with a central limit theorem on the observed objective values at the sequence of generated random measures. To further intuition, we include several illustrative examples with exact influence function calculations.},\n\tauthor = {Di Yu and Shane G. Henderson and Raghu Pasupathy},\n\tdate-added = {2025-07-23 08:14:08 -0400},\n\tdate-modified = {2025-09-24 15:41:33 -0400},\n\tjournal = {Mathematics of Operations Research},\n\tnote = {To appear},\n\ttitle = {Deterministic and Stochastic {Frank-Wolfe} Recursion on Probability Spaces},\n\turl = {https://arxiv.org/abs/2407.00307},\n\turl_paper = {https://pubsonline.informs.org/doi/abs/10.1287/moor.2024.0584},\n\tyear = {2025},\n\tbdsk-url-1 = {https://arxiv.org/abs/2407.00307}}\n\n\n
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\n Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces, made especially possible by a lemma that identifies a ``closed-form'' solution to the infinite-dimensional Frank-Wolfe sub-problem. Each iterate in dFW is expressed as a convex combination of the incumbent iterate and a Dirac measure concentrating on the minimum of the influence function at the incumbent iterate. To address common application contexts that have access only to Monte Carlo observations of the objective and influence function, we construct a stochastic Frank-Wolfe (sFW) variation that generates a random sequence of probability measures constructed using minima of increasingly accurate estimates of the influence function. We demonstrate that sFW's optimality gap sequence exhibits O(1/k) iteration complexity almost surely and in expectation for smooth convex objectives, and O(1/sqrt(k)) (in Frank-Wolfe gap) for smooth non-convex objectives. Furthermore, we show that an easy-to-implement fixed-step, fixed-sample version of (sFW) exhibits exponential convergence to epsilon-optimality. We end with a central limit theorem on the observed objective values at the sequence of generated random measures. To further intuition, we include several illustrative examples with exact influence function calculations.\n
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\n\n \n \n \n \n \n Explore then Confirm: Investment Portfolios for New Drug Therapies.\n \n \n \n\n\n \n Li, Z.; Chick, S. E.; Daems, S.; and Henderson, S. G.\n\n\n \n\n\n\n In Azar, E.; Djanatliev, A.; Harper, A.; Kogler, C.; Ramamohan, V.; Anagnostou, A.; and Taylor, S. J. E., editor(s),
Proceedings of the 2025 Winter Simulation Conference, pages 3214-3225, Piscataway, New Jersey, 2025. IEEE\n
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@inproceedings{lietal25,\n\tabstract = {New medical technologies must pass several risky hurdles, such as multiple phases of clinical trials, before\nmarket access and reimbursement. A portfolio of technologies pools these risks, reducing the collective\nfinancial risk of such development while also improving the chances of identifying a successful technology.\nWe propose a stylized model of a portfolio of technologies, each of which must pass two phases of clinical\ntrials before market access is possible. Using ideas from Bayesian sequential optimization, we study the\nvalue of running response-adaptive clinical trials to flexibly allocate resources across technologies in a\nportfolio. We suggest heuristics for the response-adaptive policy and find evidence for their value relative\nto non-adaptive policies. \n},\n\taddress = {Piscataway, New Jersey},\n\tauthor = {Zaile Li and Stephen E. Chick and Sam Daems and Shane G. Henderson},\n\tbooktitle = {Proceedings of the 2025 Winter Simulation Conference},\n\tdate-added = {2025-05-04 14:27:18 -0400},\n\tdate-modified = {2026-04-12 09:48:11 -0400},\n\teditor = {E. Azar and A. Djanatliev and A. Harper and C. Kogler and V. Ramamohan and A. Anagnostou and S. J. E. Taylor},\n\tpages = {3214-3225},\n\tpublisher = {IEEE},\n\ttitle = {Explore then Confirm: Investment Portfolios for New Drug Therapies},\n\tyear = {2025}}\n\n\n
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\n New medical technologies must pass several risky hurdles, such as multiple phases of clinical trials, before market access and reimbursement. A portfolio of technologies pools these risks, reducing the collective financial risk of such development while also improving the chances of identifying a successful technology. We propose a stylized model of a portfolio of technologies, each of which must pass two phases of clinical trials before market access is possible. Using ideas from Bayesian sequential optimization, we study the value of running response-adaptive clinical trials to flexibly allocate resources across technologies in a portfolio. We suggest heuristics for the response-adaptive policy and find evidence for their value relative to non-adaptive policies. \n
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\n\n \n \n \n \n \n The Derivative-Free Fully-Corrective Frank-Wolfe Algorithm for Optimizing Functionals Over Probability Spaces.\n \n \n \n\n\n \n Yu, D.; Pasupathy, R.; and Henderson, S. G.\n\n\n \n\n\n\n In Azar, E.; Djanatliev, A.; Harper, A.; Kogler, C.; Ramamohan, V.; Anagnostou, A.; and Taylor, S. J. E., editor(s),
Proceedings of the 2025 Winter Simulation Conference, pages 3358-3369, Piscataway, New Jersey, 2025. IEEE\n
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@inproceedings{yuhenpas25,\n\tabstract = {The challenge of optimizing a smooth convex functional over probability spaces has recently generated much attention due to its relevance in important contexts such as experimental design, emergency response, and variations of the problem of moments. For solution, the fully-corrective Frank-Wolfe (FCFW) first-order recursion has emerged as a viable and provably efficient algorithm. In this paper, we propose an FCFW recursion that rigorously handles the oft-encountered zero-order setting, where the derivative of the objective is known to exist, but only the objective at a specified probability measure is observable. The main ingredient of our proposal is an estimator for the objective's {\\em influence function}, which can be viewed as a function providing the directional derivative of the objective function in the direction of point mass probability distributions, constructed via a combination of Monte Carlo, and a projection onto the orthonormal expansion of an $L_2$ function on a compact set. An analysis of the bias and variance of the influence function estimator guides step size and Monte Carlo sample size choice, and leads to a characterization of the recursive rate behavior on smooth non-convex problems. \n},\n\taddress = {Piscataway, New Jersey},\n\tauthor = {Di Yu and Raghu Pasupathy and Shane G. Henderson},\n\tbooktitle = {Proceedings of the 2025 Winter Simulation Conference},\n\tdate-added = {2025-04-29 07:57:52 -0400},\n\tdate-modified = {2026-04-12 09:47:20 -0400},\n\teditor = {E. Azar and A. Djanatliev and A. Harper and C. Kogler and V. Ramamohan and A. Anagnostou and S. J. E. Taylor},\n\tpages = {3358-3369},\n\tpublisher = {IEEE},\n\ttitle = {The Derivative-Free Fully-Corrective {Frank-Wolfe} Algorithm for Optimizing Functionals Over Probability Spaces},\n\tyear = {2025}}\n\n\n
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\n The challenge of optimizing a smooth convex functional over probability spaces has recently generated much attention due to its relevance in important contexts such as experimental design, emergency response, and variations of the problem of moments. For solution, the fully-corrective Frank-Wolfe (FCFW) first-order recursion has emerged as a viable and provably efficient algorithm. In this paper, we propose an FCFW recursion that rigorously handles the oft-encountered zero-order setting, where the derivative of the objective is known to exist, but only the objective at a specified probability measure is observable. The main ingredient of our proposal is an estimator for the objective's \\em influence function, which can be viewed as a function providing the directional derivative of the objective function in the direction of point mass probability distributions, constructed via a combination of Monte Carlo, and a projection onto the orthonormal expansion of an $L_2$ function on a compact set. An analysis of the bias and variance of the influence function estimator guides step size and Monte Carlo sample size choice, and leads to a characterization of the recursive rate behavior on smooth non-convex problems. \n
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\n\n \n \n \n \n \n A New Convergence Analysis of Two Stochastic Frank-Wolfe Algorithms.\n \n \n \n\n\n \n Boonsiriphatthanajaroen, N.; and Henderson, S. G.\n\n\n \n\n\n\n . 2025.\n
Submitted\n\n
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@article{boohen25,\n\tauthor = {Natthawut Boonsiriphatthanajaroen and Shane G. Henderson},\n\tdate-added = {2025-04-06 12:56:30 -0400},\n\tdate-modified = {2025-04-06 12:58:12 -0400},\n\tnote = {Submitted},\n\ttitle = {A New Convergence Analysis of Two Stochastic {Frank-Wolfe} Algorithms},\n\tyear = {2025}}\n\n\n
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\n\n \n \n \n \n \n \n Frank-Wolfe Recursions for the Emergency Response Problem on Measure Spaces.\n \n \n \n \n\n\n \n Yu, D.; Henderson, S. G.; and Pasupathy, R.\n\n\n \n\n\n\n 2025.\n
Submitted.\n\n
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@unpublished{yuhenpas25b,\n\tabstract = {Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces, made especially possible by a lemma that identifies a ``closed-form'' solution to the infinite-dimensional Frank-Wolfe sub-problem. Each iterate in dFW is expressed as a convex combination of the incumbent iterate and a Dirac measure concentrating on the minimum of the influence function at the incumbent iterate. To address common application contexts that have access only to Monte Carlo observations of the objective and influence function, we construct a stochastic Frank-Wolfe (sFW) variation that generates a random sequence of probability measures constructed using minima of increasingly accurate estimates of the influence function. We demonstrate that sFW's optimality gap sequence exhibits O(1/k) iteration complexity almost surely and in expectation for smooth convex objectives, and O(1/sqrt(k)) (in Frank-Wolfe gap) for smooth non-convex objectives. Furthermore, we show that an easy-to-implement fixed-step, fixed-sample version of (sFW) exhibits exponential convergence to epsilon-optimality. We end with a central limit theorem on the observed objective values at the sequence of generated random measures. To further intuition, we include several illustrative examples with exact influence function calculations.},\n\tauthor = {Di Yu and Shane G. Henderson and Raghu Pasupathy},\n\tdate-added = {2024-06-28 11:09:17 -0400},\n\tdate-modified = {2025-07-15 09:19:01 -0400},\n\tnote = {Submitted.},\n\ttitle = {Frank-Wolfe Recursions for the Emergency Response Problem on Measure Spaces},\n\turl = {https://arxiv.org/abs/2507.09808},\n\tyear = {2025},\n\tbdsk-url-1 = {https://arxiv.org/abs/2407.00307}}\n\n\n
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\n Motivated by applications in emergency response and experimental design, we consider smooth stochastic optimization problems over probability measures supported on compact subsets of the Euclidean space. With the influence function as the variational object, we construct a deterministic Frank-Wolfe (dFW) recursion for probability spaces, made especially possible by a lemma that identifies a ``closed-form'' solution to the infinite-dimensional Frank-Wolfe sub-problem. Each iterate in dFW is expressed as a convex combination of the incumbent iterate and a Dirac measure concentrating on the minimum of the influence function at the incumbent iterate. To address common application contexts that have access only to Monte Carlo observations of the objective and influence function, we construct a stochastic Frank-Wolfe (sFW) variation that generates a random sequence of probability measures constructed using minima of increasingly accurate estimates of the influence function. We demonstrate that sFW's optimality gap sequence exhibits O(1/k) iteration complexity almost surely and in expectation for smooth convex objectives, and O(1/sqrt(k)) (in Frank-Wolfe gap) for smooth non-convex objectives. Furthermore, we show that an easy-to-implement fixed-step, fixed-sample version of (sFW) exhibits exponential convergence to epsilon-optimality. We end with a central limit theorem on the observed objective values at the sequence of generated random measures. To further intuition, we include several illustrative examples with exact influence function calculations.\n
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\n\n \n \n \n \n \n Amplification of the Power of Network Hubs and Degree Skewness over Infectious Disease Spread during Lulls.\n \n \n \n\n\n \n Cornwell, B. T.; Ji, S.; Henderson, S. G.; and Meredith, G.\n\n\n \n\n\n\n
PLOS ONE. 2025.\n
To appear\n\n
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@article{coretal24,\n\tauthor = {Benjamin T. Cornwell and Shiyu Ji and Shane G. Henderson and Gen Meredith},\n\tdate-added = {2024-03-18 07:50:12 +1030},\n\tdate-modified = {2025-10-16 07:43:41 -0400},\n\tjournal = {{PLOS ONE}},\n\tnote = {To appear},\n\ttitle = {Amplification of the Power of Network Hubs and Degree Skewness over Infectious Disease Spread during Lulls},\n\tyear = {2025}}\n\n\n
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\n\n \n \n \n \n \n \n Modeling the Impact of Community First Responders.\n \n \n \n \n\n\n \n van den Berg , P. L.; Henderson, S. G.; Jagtenberg, C. J.; and Li, H.\n\n\n \n\n\n\n
Management Science, 71(2): 992-1008. 2025.\n
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@article{berhenjagli21,\n\tabstract = {In Community First Responder (CFR) systems, traditional emergency service response is augmented by a network of trained volunteers who are dispatched via an app. A central application of such systems is out-of-hospital cardiac arrest (OHCA), where a very fast response is crucial. For a target performance level, how many volunteers are needed and from which locations should they be recruited? We model the presence of volunteers throughout a region as a Poisson point process, which permits the computation of the response-time distribution of the first-arriving volunteer. Combining this with known survival-rate functions, we deduce survival probabilities in the cardiac arrest setting. We then use convex optimization to compute a location distribution of volunteers across the region that optimizes either the fraction of incidents with a fast response (a common measure in the industry) or patient survival in the case of OHCA. The optimal location distribution provides a bound on the best possible performance with a given number of volunteers. This can be used to determine whether introducing a CFR system in a new region is worthwhile, or serve as a guide for additional recruitment in existing systems. Effective target areas for recruitment are not always obvious, since volunteers recruited from one area may be found in various areas across the city depending on the time of day; we explicitly capture this issue. We demonstrate these methods through an extended case study of Auckland, New Zealand.},\n\tauthor = {Pieter L. {van den Berg} and Shane G. Henderson and Caroline J. Jagtenberg and Hemeng Li},\n\tdate-added = {2022-12-21 05:42:30 -0500},\n\tdate-modified = {2025-02-13 12:46:16 -0500},\n\tjournal = {Management Science},\n\tnumber = {2},\n\tpages = {992-1008},\n\ttitle = {Modeling the Impact of Community First Responders},\n\turl_paper = {https://doi.org/10.1287/mnsc.2022.04024},\n\tvolume = {71},\n\tyear = {2025}}\n\n\n
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\n In Community First Responder (CFR) systems, traditional emergency service response is augmented by a network of trained volunteers who are dispatched via an app. A central application of such systems is out-of-hospital cardiac arrest (OHCA), where a very fast response is crucial. For a target performance level, how many volunteers are needed and from which locations should they be recruited? We model the presence of volunteers throughout a region as a Poisson point process, which permits the computation of the response-time distribution of the first-arriving volunteer. Combining this with known survival-rate functions, we deduce survival probabilities in the cardiac arrest setting. We then use convex optimization to compute a location distribution of volunteers across the region that optimizes either the fraction of incidents with a fast response (a common measure in the industry) or patient survival in the case of OHCA. The optimal location distribution provides a bound on the best possible performance with a given number of volunteers. This can be used to determine whether introducing a CFR system in a new region is worthwhile, or serve as a guide for additional recruitment in existing systems. Effective target areas for recruitment are not always obvious, since volunteers recruited from one area may be found in various areas across the city depending on the time of day; we explicitly capture this issue. We demonstrate these methods through an extended case study of Auckland, New Zealand.\n
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