In mathematics, a real-valued function defined on an interval is called convex (or convex downward or concave upward) if the line segment between any… (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 given… (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 in… (More)

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Highly Cited

2004

Highly Cited

2004

- Jun Zhang
- Neural Computation
- 2004

From a smooth, strictly convex function : Rn R, a parametric family of divergence function D() may be introduced: for x, y, int… (More)

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Highly Cited

2003

Highly Cited

2003

- Martin Zinkevich
- ICML
- 2003

Convex programming involves a convex set F ⊆ R and a convex function c : F → R. The goal of convex programming is to find a point… (More)

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Highly Cited

2003

Highly Cited

2003

- Hiroshi Ishikawa
- IEEE Trans. Pattern Anal. Mach. Intell.
- 2003

We introduce a method to solve exactly a first order Markov Random Field optimization problem in more generality than was… (More)

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Highly Cited

2003

Highly Cited

2003

- Daniel Pérez Palomar, John M. Cioffi, Miguel Angel Lagunas
- IEEE Trans. Signal Processing
- 2003

This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding… (More)

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Highly Cited

1999

Highly Cited

1999

- Kazuo Murota, Akiyoshi Shioura
- Math. Oper. Res.
- 1999

The concept of M-convex function, introduced recently by Murota, is a quantitative generalization of the set of integral points… (More)

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Highly Cited

1999

Highly Cited

1999

- Sebastián Ceria, João Soares
- Math. Program.
- 1999

Given a nite number of closed convex sets whose algebraic representation is known, we study the problem of optimizing a convex… (More)

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Highly Cited

1998

Highly Cited

1998

- Kazuo Murota
- Math. Program.
- 1998

A theory of “discrete convex analysis” is developed for integer-valued functions defined on integer lattice points. The theory… (More)

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Highly Cited

1997

Highly Cited

1997

- Anatoliy D. Rikun
- J. Global Optimization
- 1997

Convex envelopes of multilinear functions on a unit hypercube are polyhedral. This wellknown fact makes the convex envelope… (More)

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