Constrained optimization introduction global optimization

Minimize[{x, x^2 + y^2  < 1}, {x, y}]

{-1, {x -> -1, y -> 0}}

Minimize[{x^2, x y == 1}, {x, y}]

Minimize[{x^2, x*y == 1}, {x, y}]

Minimize[{x^2 + (y - 1)^2, y > x^2}, {x, y}]

{0, {x -> 0, y -> 1}}