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- Kees Roos, Tamás Terlaky, Jean-Philippe Vial
- Wiley-Interscience series in discrete mathematics…
- 1998

Interestingly, theory and algorithms for linear optimization an interior point approach that you really wait for now is coming. It's significant to wait for the representative and beneficial books to read. Every book that is provided in better way and utterance will be expected by many peoples. Even you are a good reader or not, feeling to read this book… (More)

- Aharon Ben-Tal, Boaz Golany, Arkadi Nemirovski, Jean-Philippe Vial
- Manufacturing & Service Operations Management
- 2005

W propose the use of robust optimization (RO) as a powerful methodology for multiperiod stochastic operations management problems. In particular, we study a two-echelon multiperiod supply chain problem, known as the retailer-supplier flexible commitment (RSFC) problem with uncertain demand that is only known to reside in some uncertainty set. We adopt a… (More)

- Jean-Louis Goffin, Jean-Philippe Vial
- SIAM Journal on Optimization
- 2000

We analyze the multiple cut generation scheme in the analytic center cutting plane method. We propose an optimal primal and dual updating direction when the cuts are central. The direction is optimal in the sense that it maximizes the product of the new dual slacks and of the new primal variables within the trust regions defined by Dikin’s primal and dual… (More)

- Kees Roos, Jean-Philippe Vial
- Math. Program.
- 1992

- Jean-Philippe Vial
- Math. Oper. Res.
- 1983

- Yurii Nesterov, Jean-Philippe Vial
- SIAM Journal on Optimization
- 1999

In this paper we consider a new analytic center cutting plane method in a projective space. We prove the eeciency estimates for the general scheme and show that these results can be used in the analysis of a feasibility problem, the variational inequality problem and the problem of constrained minimization. Our analysis is valid even for the problems whose… (More)

- Aharon Ben-Tal, Dick den Hertog, Jean-Philippe Vial
- Math. Program.
- 2015

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of… (More)

- Benjamin Jansen, Kees Roos, Tamás Terlaky, Jean-Philippe Vial
- Math. Meth. of OR
- 1996

In this paper we propose a long{step target{following methodology for linear programming. This is a general framework, that enables us to analyze various long{step primal{dual algorithms in the literature in a short and uniform way. Among these are long{step central and weighted path{following methods and algorithms to compute a central point or a weighted… (More)

- Guy de Ghellinck, Jean-Philippe Vial
- Algorithmica
- 1986

An algorithm is presented for solving a set of linear equations on the nonnegative orthant. This problem can be made equivalent to the maximization of a simple concave function subject to a similar set of linear equations and bounds on the variables. A Newton method can then be used which enforces a uniform lower bound which increases geometrically with the… (More)

- Yurii Nesterov, Jean-Philippe Vial
- Automatica
- 2008

We propose an alternative approach to stochastic programming based on MonteCarlo sampling and stochastic gradient optimization. The procedure is by essence probabilistic and the computed solution is a random variable. The associated objective value is doubly random, since it depends on two outcomes: the event in the stochastic program and the randomized… (More)