Data and performance profiles applying an adaptive truncation criterion, within linesearch-based truncated Newton...

Area of Science:

• Numerical Analysis
• Optimization Theory
• Computational Mathematics

Background:

• Large-scale unconstrained optimization problems are prevalent in various scientific and engineering fields.
• Linesearch-based truncated Newton methods offer a robust approach to solving these problems.
• Reducing inner iterations is crucial for the efficiency of these optimization methods.

Purpose of the Study:

• To present numerical data and experimental results validating a novel adaptive truncation criterion.
• To enhance the performance of linesearch-based truncated Newton methods for large-scale nonconvex optimization.
• To compare the proposed method against established techniques using standardized benchmarks and metrics.

Main Methods:

• Implementation of an adaptive truncation criterion within a linesearch-based truncated Newton framework.
• Numerical experimentation on the CUTEst test set.
• Performance profiling to compare different parameter settings.
• Comparative analysis against the TRON trust region method.

Main Results:

• The adaptive truncation criterion effectively reduces the number of inner iterations required per outer iteration.
• Performance profiles indicate competitive or superior results compared to standard parameter settings.
• The proposed linesearch-based scheme demonstrates comparable performance to the TRON trust region method.

Conclusions:

• The novel adaptive truncation criterion is a valuable enhancement for linesearch-based truncated Newton methods.
• The method shows promise for efficient large-scale nonconvex optimization.
• Further investigation into parameter tuning could yield additional performance gains.