P. Tseng, Simplified analysis of an O(nL)-iteration infeasible predictorcorrector path following method for monotone LCP, in Recent Trends in Optimization Theory and Applications, R. P. Agarwal, ed., World Scientific, Singapore, 1995, 423-434. Home/Search Document Not in Database Summary Related Articles Check |
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On Homotopy-Smoothing Methods for Variational Inequalities - Chen, Ye (7 citations) (Correct)
.... Recently, Xu and Burke [33] gave a polynomial complexity bound for an interior point smoothing method for the monotone linear complementarity problem (LCP) based on the Chen Harker Kanzow smoothing function [3, 20] and Tseng s convergence analysis for a class of infeasible interior point methods [32]. More recently, Burke Xu [2] and Hotta Yoshise [19] studied the global convergence of non interior point algorithms using the Chen Harker Kanzow smoothing function. A number of important problems in engineering and economics have both lower and or upper bounds on the variables, rather than just ....
P. Tseng, Simplified analysis of an o(nL)-iteration infeasible predictor-corrector path-following method for monotone LCP, In R.P. Agarwal ed., Recent Trends in Optimization Theory and Applications, World Scientific Press, Singapore, (1994), pp. 423-434.
A Polynomial Time Interior-Point Path-Following Algorithm for.. - Xu, Burke (1997) (6 citations) (Correct)
....central path [23] Most path following methods attempt to follow the central path by applying Newton s method to the equations F (x; y) 0 for decreasing values of . In this regard, predictor corrector strategies are the most popular due to their rapid local convergence (for examples, see [29, 31, 34, 35]) In a predictor corrector strategy a predictor step ( 0) is followed by a corrector step ( 0) to return the iterates to a pre specified neighborhood of the central path. Interior point methods stay in the vicinity of the central path and remain in the positive orthant [23] Each iterate ....
.... (x; y) fl fl fl k Psi (x; y)k 2 fl fl fl Psi (x; y) fl fl fl 2 2(1 Gamma fi) k Theta (x; y)k 2 2(1 Gamma fi) fi 2 2 2(1 Gamma fi) fi 2 2(1 Gamma fi) 2 3 The Algorithm We present an algorithm based on the interior point algorithm proposed by Tseng [29]. The global linear convergence and complexity results are stated without proof since these proofs closely parallel those provided by Tseng [29] Algorithm Choose any (fi 1 ; fi 2 ) 2 IR 2 satisfying 0 fi 1 fi 2 1; 2fi 1 1 Gamma fi 1 fi 2 ; fi 2 1 2(1 Gamma fi 1 ) 2fi 1 fi 2 ....
[Article contains additional citation context not shown here]
P. Tseng. Simplified analysis of an O(nL)--iteration infeasible predictor--corrector path--following method for monotone LCP. In R.P. Agarwal, editor, Recent Trends in Optimization Theory and Applications, pages 423---434. World Scientific Press, Singapore, 1994.
The Global Linear Convergence of a Non-Interior Path-Following.. - Burke, Xu (1997) (20 citations) (Correct)
....complexity results. Numerous variations on this basic plan have been proposed. The most notable of which are the infeasible (i.e. Mx k Gamma y k q may or may not be the zero vector) predictor corrector strategies for which local super linear convergence can also be established (e.g. see [17, 21]) Kanzow s non interior method for solving LCP(q; M) is based on the function F (x; y) Mx Gamma y q Psi (x; y) # ; 1.4) where Psi (x; y) 2 6 4 (x 1 ; y 1 ) x n ; y n ) 3 7 5 ; 1.5) and (a; b) a b Gamma q a 2 b 2 2 : 1.6) For ....
P. Tseng. Simplified analysis of an O(nL)--iteration infeasible predictor--corrector path--following method for monotone LCP. In R.P. Agarwal, editor, Recent Trends in Optimization Theory and Applications, pages 423---434. World Scientific Press, Singapore, 1994.
Search Directions And Convergence Analysis Of Some Infeasible.. - Tseng (1996) (16 citations) Self-citation (Tseng) (Correct)
....first using the predictor and corrector steps in series, in the spirit of the Mizuno Todd Ye method [22] and the second using the steps in parallel, in the spirit of Mizuno et al. McShane s method [20, 21] We describe the first method below. This is an infeasible method based on that studied in [38] for the LCP case, and it differs from other predictor corrector methods in that and Mx q Gamma y decrease in norm at both the predictor step and the corrector step. Algorithm 3.1 Choose (fi 0 ; fi 1 ; fi 2 ) 2 3 satisfying 0 fi fi 0 fi 1 fi 2 1, where fi depends on fi 0 ; fi 1 ....
P. Tseng, Simplified analysis of an O(nL)-iteration infeasible predictorcorrector path following method for monotone LCP, in Recent Trends in Optimization Theory and Applications, R. P. Agarwal, ed., World Scientific, Singapore, 1995, 423-434.
Analysis Of A Non-Interior Continuation Method Based On.. - Tseng (1998) (5 citations) Self-citation (Tseng) (Correct)
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Tseng, P., Simplified analysis of an O(nL)-iteration infeasible predictorcorrector path following method for monotone LCP, in Recent Trends in Optimization Theory and Applications, edited by R. P. Agarwal, World Scientific, Singapore, 1995, 423-434.
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