Convex Approximations of Chance Constrained Programs

By Arkadi Nemirovski, Alexander Shapiro. SIAM Journal on Optimization, 2006

1,314 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/862a46acc6a7f37834327e778abbfbe91386ef04

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Citations in the corpus

Percentile Optimization for Markov Decision Processes with Parameter Uncertainty (2010, background): “Moreover, one often does not have access to enough historical data to adequately assess the probability of a machine breaking down at a given aging stage.”
A Sampling-and-Discarding Approach to Chance-Constrained Optimization: Feasibility and Optimality (2011, background): “Yet another study about the convexity of chanceconstrained problems is [8], while convex approximations of chance-constrained problems are considered in [9, 10, 11, 12].”
Lectures on Stochastic Programming: Modeling and Theory (2009, background): “Alexander Shapiro, Darinka Dentcheva, and Andrzej Ruszczyński i i “SPbook” — 2013/12/24 — 8:37 — page vi — #6 i i i i i i i i “SPbook” — 2013/12/24 — 8:37 — page vii — #7 i i i i i i Contents Preface iii”
Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty (2012, methodology): “Our approach relies on methodologies recently dev eloped in the optimization literature and known under the name of "C hanceConstrained" (CC) optimization [9].”
Offline Policy Selection under Uncertainty (2020, background): “, 2020], then reformulate these as chance constraints to ensure ζ satisfies the constraints with high probability [Nemirovski and Shapiro, 2007].”
Optimization under Uncertainty in the Era of Big Data and Deep Learning: When Machine Learning Meets Mathematical Programming (2019, background): “In light of these computational challenges, a large body of related literature is devoted into the development of solution algorithms for chance constrained optimization problems, such as sample average approximation [68], sequential approximation [69], and convex conservative approximation schemes ”
Data-driven robust optimization (2013, neutral): “When the marginals are independent, [40] proved”
Theory and Applications of Robust Optimization (2010, background): “constraints, often called chance constraints in the literature, have a long history in stochastic optimization. Many approaches have been considered to address the computational challenges they pose ([121, 111]), including work using sampling to approximate the chance constraints [47, 45, 71]. One o”
Chance-Constrained Economic Dispatch With Non-Gaussian Correlated Wind Power Uncertainty (2017, neutral): “Recently, a number of chance-constrained optimization methods have been proposed [10]–[12].”
Data-driven chance constrained stochastic program (2015, background): “Erdoğan and Iyengar [15], Calafiore and El Ghaoui [7], Nemirovski and Shapiro [24], Vandenberghe et al.”
Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation (2018, background): “Robust optimization is often too conservative [30], while chance constrained programming is less conservative but is often NP-hard [31], [32].”
Selected topics in robust convex optimization (2007, neutral): “We are about to consider a specific Bernstein approximation originating from [56] and significantly improved in [51].”
An Actor-Critic Contextual Bandit Algorithm for Personalized Mobile Health Interventions (2017, background): “er of the two available actions. Maximizing the average reward V () subject to the stochasticity constraint (1) is a chance constrained optimization problem, an active research area in recent years (Nemirovski and Shapiro (2006); Campi and Garatti (2011)). Solving this chance constraint problem, how”
A Bilevel Model for Participation of a Storage System in Energy and Reserve Markets (2018, background): “One potential approach is to incorporate the chance constraints [17] into the offering strategy problem.”
MIMO Transceiver Design via Majorization Theory (2007, background): “An alternative emerging approach to deal with uncertainties is the so-called chance programming or probabilistic modeling [103].”
Conservative Stochastic Optimization With Expectation Constraints (2020, background): “The expectation-constrained problem in (1) has not received as much attention, though it finds applications in machine learning [17], signal processing [18], [19], communications [20], finance [21], [22], and control theory [23].”
On Ensuring that Intelligent Machines Are Well-Behaved (2017, methodology): “…constraints to hold for all P ∈ P. Scenario approximation methods can apply when P , the distribution of Wi, is neither known nor within a known set, P, but samples (realizations of Wi) can be generated from P [De Farias and Van Roy, 2004; Calafiore and Campi, 2005; Nemirovski and Shapiro, 2006].”