(i) {α - Convex Optimization

Class of problems in CS (cont’d)
(P σ ), (P τ ) and (P λ ) can all be cast as:
(P1) : min
α
f 1(α) + f 2 (α)
f 1 and f 2 are proper lsc convex functions.
(P λ )
1
2 ‖y − HΦα‖2 l 2
+ λΨ (α)
f 1 (α) = 1 2 ‖y − HΦα‖2 l 2
,f 2 (α) =λΨ (α)
(P σ )
Ψ (α) s.t. ‖y − HΦα‖ l2
≤ σ
f 1 (α) =Ψ (α) ,f 2 (α) =ı Bl2 ,σ (α)
(P τ )
1
2 ‖y − HΦα‖2 l 2
s.t. Ψ (α) ≤ τ
f 1 (α) = 1 2 ‖y − HΦα‖2 l 2
,f 2 (α) =ı Bψ,τ (α)
Stanford seminar 08-8