Convexitybowl-shapedness: function >= tangentie. f(u) >= f(w) + = f(w) + f'(w) (u - w)chord across bowl: chord >= function2nd gradient of function is psd; ▽2f(w) or, f''(w) >= 02nd gradient > 0 : strict convexityGlobal minimumconvex & the critical point (ie. gradient = 0)