The Exact Feasibility of Randomized Solutions of Uncertain Convex Programs

By Marco Claudio Campi, Simone Garatti. SIAM Journal on Optimization, 2008

605 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Ocean Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/60f8599e4174cfd075751bb2e29b068595490184

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In Management Science and Operations Research

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In Statistics and Probability

Citations in the corpus

Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, methodology): “Moreover, the optimal solution x*(ω) is guaranteed to satisfy the constraints with other unseen uncertainty realizations with a high probability [168].”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, background): “This number of support constraints is further bounded in [45] by d , the number of optimization variables, and this may introduce some conservatism.”
Distributionally Robust Optimization: A Review (2019, background): “As far as it is relevant to the scope and interest of this paper, there are two streams of research in order to handle the ambiguity about the true probability distribution and obtain a safe (or, conservative) approximation5 to (3.4)6: (1) scenario approximation scheme of (3.3) based on Monte Carlo ”
Data-driven robust optimization (2013, methodology): “First, because it leverages the concave structure of f(u,x), our approach generally yields less conservative solutions (for the same N and ) than [20].”
Linear Programming for Large-Scale Markov Decision Problems (2014, positive): “Using the re-sults on polytope constraint sampling (de Farias and Van Roy, 2004, Calaﬁore and Campi, 2005, Campi and Garatti, 2008), we reduce approximate the solution to the dual ALP with the solution to a smaller, sampled LP. Basically, de Farias and Van Roy (2004) claim that given a set of aﬃne…”
The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations (2013, background): “closed-loop cost (2) decreases. ThereforeRis usually ﬁxed to a value that is as high as admitted by the available com putational resources. 4.1 Support Rank According to the classic scenario approach [8,9], the relevant quantity for determining the sample size K for a single chance constraint (with ”