Accelerated Double Direction Method for Solving Unconstrained Optimization Problems

Algorithm 2

Calculation of direction vector 𝑑_𝑘.

Require: The stepsize 𝛼_𝑘.

 (1) 𝛼=𝛼_𝑘.

 (2)          𝑑_𝑘𝑑(𝛼)=^∗𝑘,𝑘≤𝑚−1_𝑚𝑖=2𝛼^𝑖−1𝑑^∗_{𝑘−𝑖+1},𝑘≥𝑚,

   where 𝑑^∗_𝑘 is the solution of the problem min_𝑥∈ℝΦ_𝑘(𝑑), and Φ_𝑘(𝑑) is defined by

               Φ_𝑘(𝑑)=𝑔^𝑇_𝑘1𝑑+2𝛾_𝑘+1𝐼.