This paper describes an optimization algorithm which uses up torth-order derivatives to find the optimum of anr-times continuously differentiable function of many variables. The algorithm, developed by Kalaba and Tish...
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This paper describes an optimization algorithm which uses up torth-order derivatives to find the optimum of anr-times continuously differentiable function of many variables. The algorithm, developed by Kalaba and Tishler (Ref. 1), obtains the exact values of the derivatives required for the optimization from the table algorithm presented in Kalabaet al. (Ref. 2) and Kalaba and Tishler (Ref. 3). The optimization algorithm described here reduces to the well-known newton-Raphson algorithm when only first-order and second-order derivatives are used.
This paper shows that the generalized newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of...
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This paper shows that the generalized newton algorithm [GN(r)], developed by Kalaba and Tishler (Ref. 1), can be described as a fixed-point algorithm. In addition to specifying sufficient conditions for convergence of the GN(r), we show that, forr=1, 2, 3, its rate of convergence increases with the order of the derivatives which are used.
In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in the literature. It is prov...
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In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in the literature. It is proved that the SOCAVE is equivalent to a class of second order cone linear complementarity problems (SOCLCP in short). In particular, we propose a generalizednewton method for solving the SOCAVE and show that the proposed method is globally linearly and locally quadratically convergent under suitable assumptions. We also report some preliminary numerical results of the proposed method for solving the SOCAVE and the SOCLCP, which show the efficiency of the proposed method. (C) 2010 Elsevier B.V. All rights reserved.
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