13.6-5. Consider the following linearly constrained optimization problem: Maximize f(x) = ln(X1 1) - x2^2subject to X1 2x2 ≤ 3and X1 ≤ 20, x2 ≤ 20,where ln denotes the natural logarithm. (a) Verify that this problem is a convex programming problem. (b) Use the KKT conditions to derive an optimal solution. (c) Use intuitive reasoning to demonstrate that the solution obtained in part b) is indeed optimal.

Constrained Optimization: Intuition Behind the Lagrangian

Lagrange multipliers - overview | Numerade

Session 39: Statement of Lagrange Multipliers and Example | Multivariable Calculus | Mathematics | MIT OpenCourseWare