Newton's method and its use in optimization

by: BT Polyak

European Journal of Operational Research, Vol. 181, No. 3. (16 September 2007), pp. 1086-1096.

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Abstract

Newton's method is a basic tool in numerical analysis and numerous applications, including operations research and data mining. We survey the history of the method, its main ideas, convergence results, modifications, its global behavior. We focus on applications of the method for various classes of optimization problems, such as unconstrained minimization, equality constrained problems, convex programming and interior point methods. Some extensions (non-smooth problems, continuous analog, Smale's results, etc.) are discussed briefly, while some others (e.g., versions of the method to achieve global convergence) are addressed in more details.

@article{citeulike:1650602, abstract = {Newton's method is a basic tool in numerical analysis and numerous applications, including operations research and data mining. We survey the history of the method, its main ideas, convergence results, modifications, its global behavior. We focus on applications of the method for various classes of optimization problems, such as unconstrained minimization, equality constrained problems, convex programming and interior point methods. Some extensions (non-smooth problems, continuous analog, Smale's results, etc.) are discussed briefly, while some others (e.g., versions of the method to achieve global convergence) are addressed in more details.}, author = {Polyak, B. T. }, citeulike-article-id = {1650602}, doi = {http://dx.doi.org/10.1016/j.ejor.2005.06.076}, journal = {European Journal of Operational Research}, keywords = {newton, optimization}, month = {September}, number = {3}, pages = {1086--1096}, posted-at = {2007-09-13 07:09:24}, priority = {2}, title = {Newton's method and its use in optimization}, url = {http://dx.doi.org/10.1016/j.ejor.2005.06.076}, volume = {181}, year = {2007} }

RIS record

TY - JOUR ID - citeulike:1650602 L3 - citeulike-article-id:1650602 TI - Newton's method and its use in optimization JF - European Journal of Operational Research VL - 181 IS - 3 SP - 1086 EP - 1096 N2 - Newton's method is a basic tool in numerical analysis and numerous applications, including operations research and data mining. We survey the history of the method, its main ideas, convergence results, modifications, its global behavior. We focus on applications of the method for various classes of optimization problems, such as unconstrained minimization, equality constrained problems, convex programming and interior point methods. Some extensions (non-smooth problems, continuous analog, Smale's results, etc.) are discussed briefly, while some others (e.g., versions of the method to achieve global convergence) are addressed in more details. KW - newton KW - optimization AU - Polyak, BT PY - 2007/09/16/ UR - http://dx.doi.org/10.1016/j.ejor.2005.06.076 ER -

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