Abderrahim Jourani
University of Burgundy
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Featured researches published by Abderrahim Jourani.
Siam Journal on Optimization | 2002
René Henrion; Abderrahim Jourani; Jirí V. Outrata
The paper deals with the calmness of a class of multifunctions in finite dimensions. Its first part is devoted to various conditions for calmness, which are derived in terms of coderivatives and subdifferentials. The second part demonstrates the importance of calmness in several areas of nonsmooth analysis. In particular, we focus on nonsmooth calculus and solution stability in mathematical programming and in equilibrium problems. The derived conditions find a number of applications there.
Journal of Optimization Theory and Applications | 1994
Abderrahim Jourani
In this paper, we present several constraint qualifications, and we show that these conditions guarantee the nonvacuity and the boundedness of the Lagrange multiplier sets for general nondifferentiable programming problems. The relationships with various constraint qualifications are investigated.
Mathematics of Operations Research | 1993
Abderrahim Jourani; L. Thibault
This paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in Banach spaces. These conditions are used to obtain Lagrange-Kuhn-Tucker multipliers for minimization problems with infinitely many inequality and equality constraints.
Mathematical Programming | 1990
Abderrahim Jourani; Lionel Thibault
The notion of graphical metric regularity is introduced and conditions ensuring this kind of regularity for systems of finite-dimensional multifunctions are given in terms of partial approximate subdifferentials.
Siam Journal on Control and Optimization | 2000
Abderrahim Jourani
Our aim is to present sufficient conditions ensuring Hoffmans error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffmans error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear inequality systems. In the latter case our constant may be computed explicitly.
Siam Journal on Optimization | 2002
René Henrion; Abderrahim Jourani
We study subdifferential conditions of the calmness property for multifunctions representing convex constraint systems in a Banach space. Extending earlier work in finite dimensions [R. Henrion and J. Outrata, J. Math. Anal. Appl., 258 (2001), pp. 110--130], we show that, in contrast to the stronger Aubin property of a multifunction (or metric regularity of its inverse), calmness can be ensured by corresponding weaker constraint qualifications, which are based only on boundaries of subdifferentials and normal cones rather than on the full objects. Most of the results can be immediately interpreted in the context of error bounds.
Set-valued Analysis | 1995
Abderrahim Jourani; Lionel Thibault
In this paper we give verifiable conditions in terms of limiting Fréchet subdifferentials ensuring the metric regularity of a multivalued functionF(x)=−g(x)+D. We apply our results to the study of the limiting Fréchet subdifferential of a composite function defined on a Banach space.
Journal of Optimization Theory and Applications | 1997
O. Cornejo; Abderrahim Jourani; Constantin Zălinescu
In this paper, we study conditioning problems for convex and nonconvex functions defined on normed linear spaces. We extend the notion of upper Lipschitzness for multivalued functions introduced by Robinson, and show that this concept ensures local conditioning in the nonconvex case via an abstract subdifferential; in the convex case, we obtain complete characterizations of global conditioning in terms of an extension of the upper-Lipschitz property.
Bulletin of The Australian Mathematical Society | 1993
Abderrahim Jourani; L. Thibault
This paper deals with the approximate subdifferential chain rule in a Banach space. It establishes specific results when the real-valued function is locally Lipschitzian and the mapping is strongly compactly Lipschitzian.
Numerical Functional Analysis and Optimization | 1993
Abderrahim Jourani
This paper studies the metric regularity of multivalued functions on Banach spaces, tangential approximations of the feasible set and strong sufficient optimality conditions of a parametrized optimization problem minimize The results are applied to the tangent approximations and the local stability properties of solutions of this perturbed optimization problem.