Convergence of convex-concave saddle functions: Applications to convex programming and mechanics

DOI10.1016/S0294-1449(16)30335-3zbMath0667.49009MaRDI QIDQ1117446

Hedy Attouch, Dominique Azé, Roger J.-B. Wets

Publication date: 1988

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1988__5_6_537_0

zbMATH Keywords

stabilityelasticityepi-convergencebicontinuitymultipliers of convex programs

Mathematics Subject Classification ID

Convex programming (90C25) Sensitivity, stability, parametric optimization (90C31) Inhomogeneity in solid mechanics (74E05) Methods involving semicontinuity and convergence; relaxation (49J45) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Methods of successive quadratic programming type (90C55)

Related Items

Graphical convergence of sums of monotone mappings, Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects, Consistency of statistical estimators of solutions to stochastic optimization problems, Quantitative stability analysis for maximal monotone operators and semi-groups of contractions, Epigraphical analysis, Convergence of approximate saddle points, A strong law of large numbers for random monotone operators, Shape derivatives for minima of integral functionals, Primal-dual stability in continuous linear optimization, Structural optimization of thin elastic plates: the three-dimensional approach, Analyse de récession et résultats de stabilité d'une convergence variationnelle, application à la théorie de la dualité en programmation mathématique, Generalized Second-Order Derivatives of Convex Functions in Reflexive Banach Spaces, Generalized Second Derivatives of Convex Functions and Saddle Functions, Stochastic homogenization of nonconvex integral functionals, Slice convergence: stabilité et optimisation dans les espaces non réflexifs, Subtraction theorems and approximate openness for multifunctions: Topological and infinitesimal viewpoints, Lopsided convergence: an extension and its quantification, Criteria for epi/hypo convergence of finite-valued bifunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Introduction to sensitivity and stability analysis in nonlinear programming
• Convergence des variables duales dans des problèmes de transmission à travers des couches minces par des méthodes d'épi-convergence. (Convergence of dual variables in problems of transmission through thin layers by epi-convergence methods)
• Régularization S.C.I. et \(\Gamma\)-convergence: Approximations inf- convolutives associées à un référentiel. (L.S.C. regularization and \(\Gamma\)-convergence: Inf-convolutive approximation associated with a reference functional)
• Non-homogeneous media and vibration theory
• Successive approximation and linear stability involving convergent sequences of optimization problems
• Periodic solutions and homogenization of non linear variational problems
• Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarite est bicontinue
• A general correspondence between dual minimax problems and convex programs
• Convergence of convex sets and of solutions of variational inequalities
• An extension of Fenchel's duality theorem to saddle functions and dual minimax problems
• On the continuity of the Young-Fenchel transform
• A Convergence Theory for Saddle Functions
• Local structure of feasible sets in nonlinear programming, part II: Nondegeneracy
• Continuity of the Fenchel Transform of Convex Functions
• First- and Second-Order Epi-Differentiability in Nonlinear Programming
• Mathematical methods of game and economic theory
• Preservation of Convergence of Convex Sets and Functions in Finite Dimensions
• Dual Operations on Saddle Functions
• Minimax Theorems and Conjugate Saddle-Functions.
• Convergence of Sequences of Convex Sets, Cones and Functions. II
• On the maximality of the sum of two maximal monotone operators