In Euclidean space, a convex set is the region such that, for every pair of points within the region, every point on the straight line segment thatâ€¦Â (More)

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Highly Cited

2012

Highly Cited

2012

- Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, Alan S. Willsky
- Foundations of Computational Mathematics
- 2012

In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problemâ€¦Â (More)

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Highly Cited

2010

Highly Cited

2010

- Antonin Chambolle, Thomas Pock
- Journal of Mathematical Imaging and Vision
- 2010

In this paper we study a first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-pointâ€¦Â (More)

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Highly Cited

2006

Highly Cited

2006

- Elad Hazan, Adam Tauman Kalai, Satyen Kale, Amit Agarwal
- Machine Learning
- 2006

In an online convex optimization problem a decision-maker makes a sequence of decisions, i.e., chooses a sequence of points inâ€¦Â (More)

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Highly Cited

2006

Highly Cited

2006

- Arkadi Nemirovski, Alexander Shapiro
- SIAM Journal on Optimization
- 2006

We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a givenâ€¦Â (More)

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Highly Cited

2004

Highly Cited

2004

Convex programming is a subclass of nonlinear programming (NLP) that unifies and generalizes least squares (LS), linearâ€¦Â (More)

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Highly Cited

2003

Highly Cited

2003

- Martin Zinkevich
- ICML
- 2003

Convex programming involves a convex set F âŠ† R and a convex cost function c : F â†’ R. The goal of convex programming is to find aâ€¦Â (More)

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Highly Cited

2000

Highly Cited

2000

- Ernesto G. Birgin, JosÃ© Mario MartÃnez, Marcos Raydan
- SIAM Journal on Optimization
- 2000

Nonmonotone projected gradient techniques are considered for the minimization of differentiable functions on closed convex setsâ€¦Â (More)

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Highly Cited

1996

Highly Cited

1996

- C. Bradford Barber, David P. Dobkin, Hannu Huhdanpaa
- ACM Trans. Math. Softw.
- 1996

The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convexâ€¦Â (More)

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Highly Cited

1991

Highly Cited

1991

- LÃ¡szlÃ³ LovÃ¡sz, Alexander Schrijver
- SIAM Journal on Optimization
- 1991

It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedronâ€¦Â (More)

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Highly Cited

1977

Highly Cited

1977

- Franco P. Preparata, S. J. Hong
- Commun. ACM
- 1977

The convex hulls of sets of n points in two and three dimensions can be determined with O(n log n) operations. The presentedâ€¦Â (More)

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