By M. Atteia (auth.), Prof. Dr. Werner Oettli, Prof. Dr. Diethard Pallaschke (eds.)
This voluume includes real contributions to the present learn instructions in Optimizatiton conception in addition to functions to monetary difficulties and to difficulties in business engineering. Of specific curiosity are: convex- and Nonsmooth research, Sensitivity conception, Optimization innovations for nonsmooth and Variational difficulties, regulate conception and Vector optimization. the quantity includes learn andsurvey papers. the most profit is given via an international suruvey of the country ofart of recent Optimization concept and a few regular functions.
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Extra info for Advances in Optimization: Proceedings of the 6th French-German Colloquium on Optimization Held at Lambrecht, FRG, June 2–8, 1991
81 (1981), 545-560. ABOUT THE CONVERGENCE OF THE PROXIMAL METHOD Bernard LEMAIRE Universite des Sciences et Techniques du Languedoc Place E. Bataillon, 34095 Montpellier Cedex 5 Abstract The convergence of the proximal method of Martinet- Rockafellar, in exact or approximate form, is revisited in connexion to the asymptotical behaviour of the solutions to differential inclusions associated with maximal monotone operators. Actually, in the context of convex optimization the generated sequence is shown to be minimizing without any boundedness assumption.
V,z). (y,v,w+z) ~ s + t. Taking the infimum over s,t we get the result since the inequality is obvious if one of the terms of the right hand side is m. 0 Now let us introduce the second notion of second-order derivatives we 57 intend to study. B. Hiriart-Urruty focuses about the fact that even when f is convex the quotients t -1 [f(x + tv) - [(x) - tf! (x, v)) are nonconvex functions of v in general, and their possible limits have no convexity property a priori. This led him to replace the term tfl(x,v) by •
In the sequel we consider x and v as fixed and we do not v reflect them in the notations of the conditions we introduce.
Advances in Optimization: Proceedings of the 6th French-German Colloquium on Optimization Held at Lambrecht, FRG, June 2–8, 1991 by M. Atteia (auth.), Prof. Dr. Werner Oettli, Prof. Dr. Diethard Pallaschke (eds.)