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- James V. Burke, Maijian Qian
- Math. Program.
- 2000

In previous work, the authors provided a foundation for the theory of variable metric proximal point algorithms for general monotone operators on a Hilbert space. In particular, they develop conditions for the global, linear, and super{linear convergence of their proposed algorithm. This paper focuses attention on two matrix secant updating strategies for… (More)

Let C be a nonempty closed subset of the real normed linear space X. In this paper we determine the extent to which formulas for the Clarke subdifferential of the distance for C, de(x) := inf I/Y-.rll, be< which are valid when C is convex, remain valid when C is not convex. The assumption of subdifferential regularity for d, plays an important role. When x… (More)

- Finbarr O'Sullivan, Maijian Qian
- IEEE Trans. Pattern Anal. Mach. Intell.
- 1994

Some global convergence properties of a variable metric algorithm for minimization without exact line searches, in R. 23 superlinear convergent algorithm for minimizing the Moreau-Yosida regularization F. However, this algorithm makes use of the generalized Jacobian of F, instead of matrices B k generated by a quasi-Newton formula. Moreover, the line search… (More)

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