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}]