engni assignment.docx

engni assignment.docx - PART 1(a(i Mathematical...

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PART 1 (a) (i) Mathematical optimization deals with the problem of finding numerically minimums (or maximums or zeros) of a function. In this context, the function is called cost function, or objective function, or energy. (ii) In mathematical analysis, the maximum and minimum of a function, known collectively as extreme, are the largest and smallest value of the function within the entire domain of a function (the global or absolute extreme). We say that f ( x ) has an absolute maximum at x=c if f ( x ) ≤ f ( c ) for every x in the domain we are working on. We say that f ( x ) has an absolute minimum at x=c if f ( x ) ≥ f ( c ) for every x in the domain we are working on. (iii) In mathematical analysis, the maximum and minimum of a function, known collectively as extreme, are the largest and smallest value of the function, within a given range (local or relative extreme) We say that f ( x ) has a relative (or local) maximum at x=c if f ( x ) ≤ f ( c ) for every x in some open interval around.
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