In mathematics, a function is said to be closed if for each , the sublevel set is a closed set. Equivalently, if the epigraph defined by is closedâ€¦Â (More)

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2017

2017

- Xudong Li, Defeng Sun, Kim-chuan Toh
- 2017

For a symmetric positive semidefinite linear system of equations Qx = b, where x = (x1, . . . , xs) is partitioned into s blocksâ€¦Â (More)

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2017

2017

- Li Shen, Wei Liu, Junzhou Huang, Yu-Gang Jiang, Shiqian Ma
- AAAI
- 2017

We propose a fast first-order method to solve multi-term nonsmooth composite convex minimization problems by employing a recentâ€¦Â (More)

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2017

2017

- Bo Wen, Xiaojun Chen, Ting Kei Pong
- SIAM Journal on Optimization
- 2017

In this paper, we study the proximal gradient algorithm with extrapolation for minimizing the sum of a Lipschitz differentiableâ€¦Â (More)

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2011

2011

A corollary of a celebrated theorem of Minty is that the subdifferential graph of a closed convex function on Rn has uniformâ€¦Â (More)

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2011

2011

- Emil Ernst
- 2011

Given x0, a point of a convex subset C of an Euclidean space, the two following statements are proven to be equivalent: (i) anyâ€¦Â (More)

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2005

2005

- Felipe Alvarez, Miguel Carrasco, Karine Pichard
- Math. Oper. Res.
- 2005

In order to minimize a closed convex function that is approximated by a sequence of better behaved functions, we investigate theâ€¦Â (More)

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2005

2005

- Alexandre Cabot
- SIAM Journal on Optimization
- 2005

Let Î¦0 : Rn â†’ R âˆª {+âˆž} be a closed convex function and Î¦1 : Rn â†’ R be a finite convex function that are bounded from below. Ourâ€¦Â (More)

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Highly Cited

2002

Highly Cited

2002

- Antonio Frangioni
- SIAM Journal on Optimization
- 2002

We study a class of generalized bundle methods where the stabilizing term can be any closed convex function satisfying certainâ€¦Â (More)

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1996

1996

- B. Lemaire
- 1996

The asymptotical limit of the trajectory deened by the continuous steepest descent method for a proper closed convex function fâ€¦Â (More)

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Highly Cited

1974

Highly Cited

1974

- R Tyrrell Rockafellar
- 1974

Kuhn-Tucker condition (0, 0) e dK(x, y) into a more explicit and familiar form. Writing where -k(y) = /0(x) + ylfl(xâ€¦Â (More)

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