Subgradient-projection & Bundle Methods
During the 1970s, Claude Lemaréchal and Phil. Wolfe proposed "bundle methods" of descent for problems of convex minimization. Their modern versions and full convergence analysis were provided by Kiwiel. Contemporary bundle-methods often use "level control" rules for choosing step-sizes, developing techniques from the "subgradient-projection" method of Boris T. Polyak (1969). However, there are problems on which bundle methods offer little advantage over subgradient-projection methods.
Read more about this topic: Subgradient Method
Famous quotes containing the words bundle and/or methods:
“There is Lowell, whos striving Parnassus to climb
With a whole bale of isms tied together with rhyme,
He might get on alone, spite of brambles and boulders,
But he cant with that bundle he has on his shoulders,
The top of the hill he will neer come nigh reaching
Till he learns the distinction twixt singing and preaching;”
—James Russell Lowell (18191891)
“How can you tell if you discipline effectively? Ask yourself if your disciplinary methods generally produce lasting results in a manner you find acceptable. Whether your philosophy is democratic or autocratic, whatever techniques you usereasoning, a star chart, time-outs, or spankingif it doesnt work, its not effective.”
—Stanley Turecki (20th century)