An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

Algorithm 3

Backtracking.

 INPUT: 0 < 𝛽 < 1 and 0 < 𝛾 < 0.5

 Set 𝛼 = 1

 while  𝑔(𝛼) > 𝑔(0) + 𝛼γ (∇𝜑_𝑤(𝑦_𝑙))^𝑇𝑠_𝑙𝐝𝐨

  𝛼⟵𝛽𝛼

 OUTPUT: 𝛼