Hello,
I have the functions f(x,y)=4x-3y, g1(x,y)=-2x^2-9y, g2(x,y)=4x^2+9y-72, g3(x,y)=-2x^2+9y-18 I´ve to solve the problems:
min f(x,y) with gi(x,y)<=0 i=1,2,3
max f(x,y) with gi(x,y)<=0 i=1,2,3
With the Karush-Kuhn-Tucker equations I´ve found the points:
(-6,-8) local maximum with f,g1 NO convex and g2 convex (g1,g2 active restrictions)
(6,-8) local maximum with f,g1 NO convex and g2 convex (g1,g2 active restrictions)
(-3,4) local minimum with f,g2 convex and g3 NO convex (g2,g3 active restrictions)
(3,4) local minimum with f,g2 convex and g3 NO convex (g2,g3 active restrictions)
(-3,-2) global maximum with f,g1 NO convex and g1 only active restriction
Now my doubts are that this solutions not match with the graph in which I see (-3,4) as global minimum and (6,-8) as global maximum. Then I don´t know if sufficient conditions for global optimum includes only active restrictions or all restrictions.
Thanks