A crucial interface between Optimization theory, Trace theory, and Lie Symmetry theory is brought to the fore in this paper, as an enhancement of standard known results established in Partial Differen...Journal of Mathematics and Statistics, Published online: 2025-01-22; doi:10.3844/jmssp.2025.1.72025-01-22 DOI: 10.3844/jmssp.2025.1.7