Subgradient method: Difference between revisions

Revision as of 09:05, 12 March 2010

Revision as of 01:10, 8 October 2010

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'''Subgradient methods''' are [[iterative method]]s for solving [[convex optimization|convex minimization]] problems. Originally developed by [[Naum Z. Shor]] and others in the 1960s and 1970s, subgradient methods canare beconvergent usedwhen withapplied even to a non-differentiable objective function. When the objective function is differentiable, subgradient methods for unconstrained problems use the same search direction as the method of [[gradient descent|steepest descent]].

Although subgradient methods can be much slower than [[interior-point methods]] and [[Newton's method in optimization|Newton's method]] in practice, they can be immediately applied to a far wider variety of problems and require much less memory. Moreover, by combining the subgradient method with primal or dual decomposition techniques, it is sometimes possible to develop a simple distributed algorithm for a problem.