Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0667.49009
Azé, Dominique; Attouch, Hedy; Wets, Roger J.-B.
Convergence of convex-concave saddle functions: Applications to convex programming and mechanics. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 5, No.6, 537-572 (1988). ISSN 0294-1449

In the framework of the epi-convergence theory the authors generalize to reflexive Banach spaces some results on the bicontinuity with respect to the epitopology of the Legendre-Fenchel transform on the space of proper, lower semicontinuous, convex functions defined on $R\sp n.$ \par It is shown that the appropriate notion of convergence for saddle function is that of epi/hypo-convergence. \par The results are applied to study the stability of the optimal solutions and associated multipliers of convex programs. Applications in mechanics are also considered. \par The first one concerns homogenization of elasticity, where primal and dual variable are respectively equal to displacement vector fields and stress tensor fields. The homogenization process is studied by introduction of the associated Lagrangians, with their epi/hypo- convergence that provides the convergence of their saddle points. The second one deals with the convergence of the primal/dual solutions in a reinforcement problem when the thickness of the reinforced zone goes to zero.
[M.Codegone]

MSC 2000:: *49J45 Optimal control problems inv. semicontinuity and convergence
74E05 Inhomogeneity
90C25 Convex programming
90C31 Sensitivity, etc.
90C55 Methods of successive quadratic programming type
54A20 Convergence in general topology

Keywords: epi-convergence; bicontinuity; stability; multipliers of convex programs; elasticity

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]