Indeed max {f(x): x in X} = - min {-f(x): x in X} However, gradient ascent on a convex minimization problem will get stuck in a local maximum (as a convex m

Indeed max {f(x): x in X} = - min {-f(x): x in X} However, gradient ascent on a convex minimization problem will get stuck in a local maximum (as a convex minimization problem has f(x) convex, hence with local minima = global minima), and viceversa for gradient descent algorithms on concave maximization problems.