(A) simplified projection scheme applied to subgradient method

Abstract

The optimization problem of a convex, not necessarily differentiable function under linear constraints is considered in this thesis. For this problem the conventional subgradient method has a weakness in that the involved projection step requires a heavy computational burden when the number of constraints is large. We have developed numerical methods with special attention to the computational efficiency. The suggested methods have simplified the involved projection to reduce computational requirement considerably while preserving the simplicity of the algorithm. Some related properties of our search direction are provided. Our computational results show a improvement in computational efficiency over Poljak``s method. Furthermore it is discussed that our methods can be applied as an efficient optional rule to avoid the heavy computational load in implementing the improved subgradient method of Poljak.