Solvability Analysis Of Equality-Constrained Optimization Problems With Nonlinear Functions

This paper attempts fresh review techniques for solving constrained optimization problems with non-linear functions, emphasizing the Lagrange multipliers method. The paper reviews their solvability ability as employed in solving equality-constrained optimization problems. The first and second-order necessary conditions for obtaining optimal solutions are stated and discussed in this paper. The method of Lagrange multiplier was used to solve for optimal points. The work also demonstrates how the Borded Hessian Matrix can be used to determine the optimal solution to non-linear equality constraint problems with many constraints.