Intensity modulated radiation therapy (IMRT) is one of radiation therapies for cancers, and it is considered to be effective for complicated shapes of tumors, since dose distributions from each irradiation can be modulated arbitrary. Fluence map optimization (FMO), which optimizes beam intensities with given beam angles, is often formulated as an optimization problem with dose … Read more
We extend the notion of globalized robustness to consider distributional information beyond the support of the ambiguous probability distribution. We propose the globalized distributionally robust counterpart that disallows any (resp., allows limited) constraint violation for distributions residing (resp., not residing) in the ambiguity set. By varying its inputs, our proposal recovers several existing perceptions of … Read more
The European natural gas market is undergoing fundamental changes, fostering uncertainty regarding both supply and demand. This uncertainty is concentrated in the value of strategic infrastructure investments, e.g., projects of common interest supported by European Union public funds, to safeguard security of supply. This paper addresses this matter by suggesting an adaptive robust optimization framework … Read more
A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more
Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due … Read more
Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks with binary activation functions and continuous or integer weights (BDNN). We show that the BDNN can be reformulated as a … Read more
We propose a generic model for the capacitated vehicle routing problem (CVRP) under demand uncertainty. By combining risk measures, satisficing measures or disutility functions with complete or partial characterizations of the probability distribution governing the demands, our formulation bridges the popular but often independently studied paradigms of stochastic programming and distributionally robust optimization. We characterize … Read more
This paper considers contextual stochastic optimization with endogenous uncertainty, where random outcomes depend on both contextual information and decisions. We analyze the statistical properties of solutions from two prominent approaches: predict-then-optimize (PTO), which first predicts a model between outcomes, contexts, and decisions, and then optimizes the downstream objective; and estimate- then-optimize (ETO), which directly estimates … Read more
Consider a seller seeking a selling mechanism to maximize the worst-case revenue obtained from a buyer whose valuation distribution lies in a certain ambiguity set. For a generic convex ambiguity set, we show via the minimax theorem that strong duality holds between the problem of finding the optimal robust mechanism and a minimax pricing problem … Read more
We investigate the concept of adjustability — the difference in objective values between two types of dynamic robust optimization formulations: one where (static) decisions are made before uncertainty realization, and one where uncertainty is resolved before (adjustable) decisions. This difference reflects the value of information and decision timing in optimization under uncertainty, and is related … Read more