Monte Carlo sampling-based methods for stochastic optimization

By Tito Homem-de-Mello, Güzin Bayraksan. 2014

327 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Probabilistic & Bayesian Methods, Mathematical Optimization

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Citations in the corpus

Stochastic optimization models for location and inventory prepositioning of disaster relief supplies (2020, methodology): “…+ ∑ (i,j)∈A ∑ l∈L [ V i,j,l ( η∗i,j,l +$ ∗ i,j,l − τi,j,l ) + ∆Vi,j,l ( Φ∗i,j,l + Λ ∗ i,j,l − %∗i,j,lτi,j,l ) + ∑ (i,j)∈A [( ψ∗i,j − ∑ l∈L η∗i,j,l ) V̂i,j + ( ϕ∗i,j − ∑ l∈L $∗i,j,l ) V̂i,j ] − ∑ i∈I ∑ l∈L q∗i,lλi,l } end if Numbers and Shapiro (2003), we have F̂N → F with probability one (w.p.1)…”
Distributionally Robust Optimization: A Review (2019, background): “Assessing the quality of this solution is well-studied in the context of SO, see, e.g., Bayraksan and Morton [14, 15], Homem-De-Mello and Bayraksan [147].”
Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning (2019, unknown): “In decision analysis this phenomenon is sometimes termed the optimizer’s curse [101], and in stochastic optimization it is referred to as the optimization bias [27, 99].”
Chance-Constrained Generic Energy Storage Operations Under Decision-Dependent Uncertainty (2022, methodology): “We employ the standard reformulation from [11], and yields: Where normalized inverse cumulative distribution function F − 1 can be obtained by Monte Carlo sampling (MCS) [33] of any kind of distribution (e.g., normal distribution, beta distribution).”
Constrained Learning With Non-Convex Losses (2021, background): “This approach is grounded on celebrated generalization results from learning [3]–[5] and stochastic optimization theory [6], [7] showing that under mild conditions, the ERM solutions are close to their statistical analog for large enough sample sizes.”