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- J V Burke, Maijian Qian
- 1997

The Proximal Point Algorithm (PPA) is a method for solving inclusions of the form 0 2 T (z) where T is a monotone operator on a Hilbert space. The algorithm is one of the most powerful and versatile solution techniques for solving variational inequalities, convex programs, and convex{concave mini{max problems. It possesses a robust convergence theory for… (More)

- 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

- J V Burke, Maijian Qian
- 1998

Interest in the variable metric proximal point algorithm (VMPPA) is fueled by the desire to accelerate the local convergence of the proximal point algorithm without requiring the divergence of the proximation parameters. In this paper, the local convergence theory for matrix secant implementations of the VMPPA is applied to a globally convergent… (More)

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