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Constrained Optimization . Economics 214 Lecture 41. 2 nd Order Conditions Constrained Optimization . Sufficient conditions in optimization problems require determining The sign of the second total differential. The sign of the second Total differential of a Lagrangian function.
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Constrained Optimization Economics 214 Lecture 41
2nd Order Conditions Constrained Optimization Sufficient conditions in optimization problems require determining The sign of the second total differential. The sign of the second Total differential of a Lagrangian function Depends on the sign of the determinant of the bordered Hessian of the Lagrangian function.
Bordered Hessian for Bivariate Function The Bordered Hessian for the Lagrangian function
2nd Order Conditions for Maximum • Sufficient Condition for a Maximum in the Bivariate Case with one Constraint: A Lagrangian function is negative definite at a stationary point if the determinant of its bordered Hessian is positive when evaluated at that point. In this case the stationary point identified by the Lagrange multiplier method is a maximum.
2nd Order Condition for Minimum • Sufficient Condition for a minimum in the Bivariate Case with one Constraint: A Lagrangian function is positive definite at a stationary point if the determinant of its bordered Hessian is negative when evaluated at that point. In this case the stationary point identified by the Lagrange multiplier method is a minimum.
