Optimization: Proceedings of the 9th Belgian-French-German Conference on Optimization Namur, September 7–11, 1998Van Hien Nguyen, Jean-Jacques Strodiot, Patricia Tossings The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding members of the Conference. Hence the name: Belgian French-German Conference on Optimization. Since the very beginning, the purpose of these Conferences has been to bring together researchers working in the area of Optimization and partic ularly to encourage young researchers to present their work. Most of the participants come from the organizing countries. However the general ten dancy is to invite outside researchers to attend the meeting. So this year, among the 101 participants at this Conference, twenty researchers came from other countries. The general theme of the Conference is everything that concerns the area of Optimization without specification of particular topics. So theoretical as pects of Optimization, in addition to applications and algorithms of Opti mization, will be developed. However, and this point was very important for the organizers, the Conference must retain its convivial character. No more than two parallel sessions are organized. This would allow useful contacts between researchers to be promoted. The editors express their sincere thanks to all those who took part in this Conference. Their invaluable discussions have made this volume possible. |
Contents
| 1 | |
The heavy ball with friction dynamical system for convex con | 25 |
Vector variational principles towards asymptotically well | 55 |
Tangential regularity of Lipschitz epigraphic setvalued map | 69 |
Relaxed assumptions for iteration methods | 83 |
Eigenvalue localization for multivalued operators | 111 |
Formulating and solving nonlinear programs as mixed com | 132 |
Convergence analysis of a perturbed version of the 0scheme | 149 |
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algorithm Analysis analytic center applied approximation assume assumption augmented Lagrangian Banach spaces bounded closed convex computational cone consider constraints convergence Convex Analysis convex function convex programming convex set decomposition defined definition denote derivatives differentiable distance geometry dynamic equivalent exists feasible finite fixed point function f global hence Hilbert space iteration K₁ Lagrangian Lemma lim sup linear Lipschitz Lipschitz continuous lower semicontinuous Math Mathematical Programming matrix maximal monotone operator method minimization monotone operator nonconvex nonempty nonexpansive nonlinear nonlinear programming nonsmooth norm objective function obtain optimality conditions optimization problems parameters perturbed Proof properties Proposition proximal quadratic random lsc functions Rockafellar satisfied sequence set-valued mapping SIAM solver solving Stochastic Programming Theorem Tikhonov regularization tion variables variational inequality vector vertex vn+1 weakly efficient