Accelerated Double Direction Method for Solving Unconstrained Optimization Problems

Algorithm 1

Calculation of the step length 𝛼_𝑘 by reducing the curve search rule from [1] to the backtracking line search starting from 𝛼=1.

Require: Objective function 𝑓(𝑥), the direction 𝑑_𝑘 of the search at the point 𝑥_𝑘 and numbers 0<𝜎<0.5 and 𝛽∈(𝜎,1).

 (1) Set 𝛼=1

 (2) while 𝑓(𝑥_𝑘+𝛼𝑑_𝑘)>𝑓𝑥_𝑘+𝜎𝛼𝑔^𝑇_𝑘𝑑_𝑘 take 𝛼∶=𝛼𝛽

 (3) Return 𝛼_𝑘=𝛼.