A modified simplex based direct search optimization algorithm for adaptive transversal FIR filters.

Area of Science:

• Optimization Algorithms
• Computational Mathematics
• Signal Processing

Background:

• The Nelder-Mead (NM) method is a widely used optimization technique.
• NM suffers from convergence issues in higher-dimensional and complex problems.
• Existing NM implementations use fixed parameters for reflection and expansion steps.

Purpose of the Study:

• To present a novel modified optimization algorithm combining Nelder-Mead with a gradient-based approach.
• To address NM's convergence issues by modifying simplex regeneration and parameter selection.
• To improve convergence speed and accuracy in higher-dimensional optimization problems.

Main Methods:

• A modified optimization algorithm is proposed, integrating Nelder-Mead with gradient-based optimization.
• The algorithm dynamically reshapes the simplex at each iteration based on the objective function.
• Optimal reflection and expansion parameters are computed iteratively, with the simplex centroid regenerated at this optimum.

Main Results:

• The modified algorithm exhibits faster convergence than the standard Nelder-Mead method for lower-dimensional problems.
• The proposed technique shows good convergence for higher-dimensional problems, such as those with many filter taps.
• Comparative analysis against stochastic methods like LMS and NLMS demonstrates competitive performance and improved accuracy.

Conclusions:

• The modified optimization algorithm effectively overcomes the convergence limitations of the traditional Nelder-Mead method.
• The technique provides a robust solution for real-time implementation in adaptive filters and complex identification problems.
• The enhanced algorithm guarantees acceptable convergence and improved accuracy, particularly for higher-dimensional challenges.