Research on a Class of Optimization Problems of Higher Education Cost with Cobb–Douglas Constraint Condition

This study focuses on a class of optimization problems about higher education costs with industrial production characteristics, in which the objective function is a quadratic cost function and the nonlinear constraints follow the Cobb–Douglas form. Through variable substitution, this class of nonlinear-constrained optimization problems is converted into optimization problems with linear constraints. Further, this study derives the conditions for the existence of optimal solutions to this optimization problem and conducts numerical simulations for the two-variable scenario to demonstrate its applicability in the field of higher education.