Hi,
Please consider an function f(x,y) to be maximize. To get a unique (x*,y*) at which this function get maximized we will assume the hessian matrix to be negative definite.
Case 1: Principal minors of H are functions of parameters
Where H is equal to
D[f(x,y), {{x,y},2]
Case 2: Principal minors of H are functions of x & y
And principal minors resulted into two conditions of form:
g(x,y)>0 && h(x,y)>0
My question: Do we use KKT conditions to find the optimum solution for case 2? Hence, following modification will be made in Maximize[ ] for case 1 and case 2 respectively.
For case 1:
Maximize[f(x,y), {x,y}]
and
For case 2:
Maximize[{f(x,y), g(x,y)>0 && h(x,y)>0 }, {x,y}]