Let us call methods based on differential calculus the analytic methodsMethodanalytic. Sometimes, applying these methods is called nonlinear programming, as they can find the minima or maxima of a nonlinearFunctionobjective objective functionFunctionobjectivenon-linear. Solutions to one-dimensionalProblemunconstrainedone-dimensional unconstrainedProblemunconstrained problemsProblemunconstrainedmulti-dimensional and multi-dimensional unconstrained andProblemconstrained constrained problemsProblemconstrainedmulti-dimensional are provided to readers in this chapter. Equality and inequality constraintsConstraintsinequality are presented separately since both problems require different techniques and approaches.