PART 1a) )Mathematical optimization deals with the problem of fnding numerically minimums or ma!imums or zeros) of a function" #n this conte!t$ the function is called cost function$ or energy")#n mathematical analysis% the ma!ima and minima the plural of ma!imum and minimum) of a function$ &nown collecti'ely as e!trema the plural of e!tremum)$ are the largest and smallest 'alue of the function within the entire domain of a function the global or absolute e!trema)"(e say that f!) has an absolute or global) ma!imum at !)c if f!) * fc) for e'ery ! in the domain we are wor&ing on"(e say the f!) has an absolute or global) minimum at !)c if f!) + fc) for e'ery ! in the domain we are wor&ing on") #n mathematical analysis$ the ma!ima and minima the plural of ma!imum and minimum) of a function$ &nown collecti'ely as e!trema the plural of e!tremum)$ are the largest and smallest 'alue of the function$ within a gi'en range the local or relati'e e!trema)"(e say the f!) has a relati'e or local) ma!imum at !)c if f!) * fc) fore'ery ! in some open inter'al around"(e say the f!) has a relati'e or local) minimum at !)c if f!) + fc) for e'ery ! in some open inter'al around"