Struggling with large-scale optimization problems? This paper introduces FORTRAN 77 software for implementing the Spectral Projected Gradient (SPG) method, a nonmonotone algorithm designed for solving convex-constrained optimization challenges. The algorithm combines the classical projected gradient approach with a spectral gradient steplength selection and a nonmonotone line-search strategy. SPG requires user-provided values for the objective function and its gradient, as well as projections onto the feasible set. The spectral gradient method enhances efficiency by dynamically adjusting the steplength, while the nonmonotone line search allows for occasional increases in the objective function to escape local minima. The projected gradient method ensures that each iterate remains within the feasible set by projecting it onto the boundary. Recent numerical tests on very large location problems demonstrate SPG's superior efficiency compared to existing general-purpose software, particularly when projections can be computed efficiently. This research provides a valuable tool for researchers and practitioners dealing with computationally intensive optimization tasks.
Published in ACM Transactions on Mathematical Software, this paper fits squarely within the journal's focus on providing high-quality, reliable software tools for mathematical problem-solving. The SPG algorithm, detailed in the paper, represents a significant contribution to the field of optimization, offering an efficient solution for large-scale convex-constrained problems. The numerous citations this paper has received underscore its impact and relevance to the journal's audience.