D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems, SIAM J. Optim., 7 (1997), pp. 463--480. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Globally Convergent Broyden-like Methods for Semismooth.. - Li, Fukushima (1999) (Correct)
....problem that possesses global and superlinear convergence properties. We refer to [14] and [31] for reviews about Newton type methods for nonsmooth and semismooth equations. Local convergence of quasi Newton methods for nonsmooth and semismooth equations has also been studied by some authors [3, 4, 17, 21, 28, 33]. There are a few papers that deal with globally convergent quasi Newton methods for semismooth equations arising from nonlinear complementarity problems and mixed complementarity problems [24, 26, 35] In [26] by using a splitting technique of [30] a well defined quasi Newton method that ....
D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems, SIAM J. Optim., 7 (1997), 463-480.
Global and Superlinear Convergence of the Smoothing Newton.. - Chen, Qi, Sun (1998) (12 citations) Self-citation (Sun) (Correct)
....Jacobian of H at x in the sense of Clarke [7] is H(x) conv B H(x) The superlinear convergence of (1. 10) is established for these two kinds of generalized Jacobians in [40, 43] For the need of algorithms, some other variants of Jacobians and their perturbations are used in the literature [48, 49, 51]. A general range 6 X. Chen, L. Qi, D. Sun of different kinds of generalized Jacobians, which are associated with superlinear convergence of (1.10) is discussed in [41] In this paper, for the function F , we use a kind of generalized Jacobians, denoted as C F and defined as C F (x) F 1 ....
....Newton method is for the variational inequality problem (1.3) with X given by X = fx 2 R n j g(x) 0; h(x) 0; l x ug; where g : R n R m1 and h : R n R m2 are assumed to be twice continuously differentiable. The Karush Kuhn Tucker conditions of problem (1. 3) can be written as [49] 0 B B B B B B x Gamma Pi [l;u] x Gamma L(x; Gamma Pi R n [ Gamma ( Gammag(x) Gammah(x) 1 C C C C C C A = 0; 5.3) where L(x; p(x) m 1 X i=1 rg i (x) i m 2 X j=1 rh j (x) j : Problem (5.3) is a special box constrained variational inequality ....
D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems, SIAM J. Optim., to appear.
A New Look at Smoothing Newton Methods for Nonlinear.. - Qi, Sun, Zhou (1997) (6 citations) Self-citation (Sun) (Correct)
.... because if in (1) the set X is not of the form (2) but is represented by several equalities and inequalities, then under standard constraint qualifications [25] we can equivalently transform (1) into new VIs with the constraint set of form (2) possibly with increased dimension (see, e.g. [54]) When X = # n , the VIs reduce to the nonlinear complementarity problem (NCP for abbreviation) Find y # # # n such that F (y # ) # # n and F (y # ) T y # = 0. 3) It is well known (see, e.g. 25] that solving (1) is equivalent to finding a root of the following equation: W ....
D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems, SIAM Journal on Optimization 7 (1997) 463-- 480.
Nonsmooth Equations and Smoothing Newton Methods - Qi, Sun (1998) (1 citation) Self-citation (Sun) (Correct)
....= 0: So, if H 0 (x; d) exists, then (2.2) implies that for any V 2 H(x d) d 0, V d Gamma H 0 (x; d) o(kdk) Hence (2.2) implies the semismoothness of H at x if H 0 (x; d) exists. On the other hand, the semismoothness of H at x implies (2. 2) since H 0 (x; d) exists in this case [Page 465, SuH97]. Note that the nonsingularity of H(x ) in the above theorem is somewhat restrictive in some cases. Qi [Qi93] presented a modified version of (2.1) which may be stated as follows x k 1 = x k Gamma V Gamma1 k H(x k ) 2.3) where V k 2 B H(x k ) The difference of this version ....
D. Sun and J. Han, "Newton and quasi-Newton methods for a class of nonsmooth equations and related problems", SIAM Journal on Optimization, 7 (1997) 463--480.
Secant Methods for Semismooth Equations - Potra, Qi, Sun (1998) (1 citation) Self-citation (Sun) (Correct)
....establish superlinear convergence for secant methods for solving general semismooth equations. Fortunately, in practice, most semismooth equations have the structure studied in this paper. We note that for special composite semismooth equations, quasi Newton methods have been discussed in [21] [26], 8] By considering the discussion given in Section 5, we may generalize the quasi Newton methods discussed in the above cited papers to composite semismooth equations of the form (5.1) or (5.2) For general nonsmooth equations, differentiability at the solution has to be assumed in order to ....
D. Sun and J. Han. Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM Journal on Optimization. to appear.
An Infeasible Primal-Dual Algorithm for TV-Based.. - Hintermüller, Stadler (2004) (Correct)
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D. Sun and J. Han, Newton and quasi-Newton methods for a class of nonsmooth equations and related problems, SIAM J. Optim., 7 (1997), pp. 463--480.
On the Convergence of the Newton Iteration - Veselic (Correct)
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Sun, D., Han, J., Newton and Quasi-Newton Methods for a class of Nonsmooth Equations and Related Problems, SIAM J. Optim. 7 (1997) 463-480.
Numerical Methods for Nonlinear Equations in Option Pricing - Pooley (2003) (Correct)
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D. Sun and J. Han. Newton and quasi-Newton methods for a class of nonsmooth equations and related problems. SIAM Journal on Optimization, 7:463--480, 1997.
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