robust optimisation Flashcards
(25 cards)
Q:Define violation probability for a scenario solution x_m*
A:P({δ∈Δ | g(x_m*
Q:What does the symbol “:” mean inside P(δ:g(x_m*
δ)>0)?
Q:State the PAC guarantee for a compression set of size d
A:P^m({δ_1…δ_m | P(δ∈T\H_m)≤ε})≥1−(m choose d)(1−ε)^{m−d}
Q:How many support constraints exist in a nondegenerate convex scenario program with n_x decisions
A:At most n_x
Q:Give the stronger binomial tail bound when the compression set is unique
A:q(m
Q:Formula to choose m for confidence β and violation ε in convex case
A:m≥(2/ε)(d−1+ln(1/β))
Q:Expected violation bound for convex scenario programs
A:E≤d/(m+1)
Q:Number of samples for expected violation ≤ρ
A:m≥d/ρ−1
Q:Decision variables count for epigraphic min–max with n_x variables
A:d=n_x+1
Q:Lyapunov LMI for closed loop stability with feedback K
A:(A(δ)+B(δ)K)^TP+P(A(δ)+B(δ)K)≺0
Q:Reparameterization used to linearize LMI in scenario control design
A:Set Z=KP
Q:Violation probability wording
A:Probability that new δ breaks the constraint
Q:Define hypothesis H_m in scenario approach
A:H_m={δ∈Δ | g(x_m*
Q:Define target set T in learning view
A:T is the true feasible uncertainty set
Q:Compression set definition
A:Subset of samples whose hypothesis equals H_m
Q:What is Δ in uncertain optimization
A:The space of all uncertainty realizations
Q:Objective of minimum width interval problem
A:Minimize upper bound minus lower bound
Q:Constraint form for vertical strip width problem
A:|y_i−(x_2u_i+x_3)|≤x_1
Q:Radius decision variable in minimum disk problem
A:x_1
Q:Support constraint meaning
A:Removing it changes the optimum
Q:Confidence meaning in PAC context
A:Probability that violation bound holds
Q:Violation level ε meaning
A:Maximum tolerated probability of constraint breach
Q:Symbol P^m meaning
A:Product probability over m independent samples
Q:Scenario program basic form
A:Minimize c^Tx subject to g(x
