Global optimization tailored for graphics processing units: Complete and rigorous search for large-scale nonlinear...

Area of Science:

• Numerical Analysis
• Optimization
• High-Performance Computing

Background:

• Global optimization of nonlinear functions is computationally challenging.
• Existing methods struggle with large-scale problems and guaranteed enclosure of the global minimum.
• Interval analysis provides rigorous bounds but can be computationally intensive.

Purpose of the Study:

• To introduce an efficient and guaranteed numerical method for enclosing the global minimum of nonlinear functions.
• To leverage graphics processing unit (GPU) architecture for accelerating global optimization.
• To address the limitations of existing methods in handling high-dimensional and complex objective functions.

Main Methods:

• Utilizes interval analysis for rigorous bounding of function minima.
• Employs a novel GPU-based single program, single data (SPSD) parallel programming style to overcome performance bottlenecks.
• Integrates a variable cycling technique to reduce computational cost for large-scale problems.

Main Results:

• The method successfully encloses the guaranteed global minimum for 11 benchmark test functions.
• Achieved high-dimensional (up to 10,000 dimensions) global minimum enclosure, exceeding previously reported literature.
• Demonstrated efficient computation using a single GPU within reasonable timeframes.

Conclusions:

• The developed method offers a robust and efficient solution for global optimization problems.
• GPU acceleration and novel programming techniques significantly enhance performance for large-scale nonlinear function minimization.
• This approach advances the state-of-the-art in guaranteed global optimization for challenging benchmark functions.