Arjun Ramachandra
Welcome to my homepage
Summary
My research is broadly focused on incorporating realistic dependence models in distributionally robust optimization problems with structured objective functions. Most traditional approaches tackling such problems assume the random inputs to be independent, while in reality, more complex notions of dependence are often encountered. In particular, I explore the behaviour of discrete functions under various dependence models such as uncorrelated random input, worst-case correlations (when only the marginal distributions of the random inputs are available) and limited dependence, leading to useful insights on the interplay between randomness and function structure. As a result, I also derive optimal solutions or worst-case performance guarantees to otherwise hard distributionally robust optimization problems. The list of my publications and preprints is below.
Publications
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Tight probability bounds with pairwise independence, with Karthik Natarajan, , SIAM Journal on Discrete Mathematics, 37(2), 516-555, 2023. link
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Extremal probability bounds in combinatorial optimization, with Divya Padmanabhan, Selin Damla Ahipasaoglu and Karthik Natarajan, SIAM Journal on Optimization, 32(4), 2828-2858, 2022. link
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Probability bounds for n random events under (n-1)-wise independence, with Colin Tan and Karthik Natarajan, Operations Research Letters, 51(1), 116-122, 2023. link
Preprints
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Distributionally robust optimization through the lens of submodularity, with Divya Padmanabhan and Karthik Natarajan, available on arXiv (2312.04890), 2024 link
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Submodularity and pairwise independence, with Karthik Natarajan, preprint available on arXiv (2209.08563). 2022, link
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Robust conic satisficing, with Napat Rujeerapaiboon and Melvyn Sim, preprint available on arXiv (2107.06714). 2021, link
Thesis
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Towards tightness with pairwise independence, extremal dependence and robust satisficing using linear and conic duality, PhD Thesis, National University of Singapore (NUS) Scholar Bank, 10635/204937, 2021. link
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