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In the class of unconstrained (or equality-constrained) problems, the simplest ones are those in which the objective is [[Quadratic programming|quadratic]]. For these problems, the [[KKT conditions]] (which are necessary for optimality) are all linear, so they can be solved analytically.<ref name=":2" />{{Rp|___location=chpt.11}}
For unconstrained (or equality-constrained) problems with a general convex objective that is twice-differentiable, [[Newton's method in optimization|Newton's method]] can be used. It can be seen as reducing a general unconstrained convex problem, to a sequence of quadratic problems.<ref name=":2" />{{Rp|___location=chpt.11}}Newton's method can be combined with [[line search]] for an appropriate step size, and it can be mathematically proven to converge quickly.
Other efficient algorithms for unconstrained minimization are [[gradient descent]] (a special case of [[Method of steepest descent|steepest descent]]).
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