scientific article

Publication date: 1986

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

convex functions subgradient closed range theorem Slater condition Fenchel-Legendre transform infimum-convolution non reflexive Banach spaces Banach-Dieudonné-Krein-Smulian theorem

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Duality theory (optimization) (49N15) Duality theory for topological vector spaces (46A20) Optimality conditions for minimax problems (49K35) Convex sets in topological linear spaces; Choquet theory (46A55) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items

A representation of maximal monotone operators by closed convex functions and its impact on calculus rules ⋮ Some formulae of convex and nonconvex duality ⋮ Optimality theorems for linear fractional optimization problems involving integral functions defined on Cn [0,1] ⋮ Regularization graphs—a unified framework for variational regularization of inverse problems ⋮ The relevance of convex analysis for the study of monotonicity ⋮ Infimal convolution regularisation functionals of BV and \(\mathrm{L}^p\) spaces. I: The finite \(p\) case ⋮ A Comparison of Some Recent Regularity Conditions for Fenchel Duality ⋮ Weaker conditions for subdifferential calculus of convex functions ⋮ Risk Trading and Endogenous Probabilities in Investment Equilibria ⋮ On a decomposition formula for the proximal operator of the sum of two convex functions ⋮ Moreau's decomposition in Banach spaces ⋮ A function space framework for structural total variation regularization with applications in inverse problems ⋮ Forward-backward splitting with Bregman distances ⋮ The occasional distributivity of ∘ over+e and the change of variable formula for conjugate functions ⋮ Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization ⋮ Total variation regularization of multi-material topology optimization ⋮ Extremality of convex sets with some applications ⋮ Some Functional Analytic Tools for Utility Maximization ⋮ Abstract nonlinear evolution inclusions of second order with applications in visco-elasto-plasticity ⋮ Differential stability of convex optimization problems with possibly empty solution sets ⋮ A new approach to constrained total variation solvation models and the study of solute-solvent interface profiles ⋮ Alternating forward-backward splitting for linearly constrained optimization problems ⋮ Higher-Order Total Directional Variation: Analysis ⋮ The Brezis-Browder theorem in a general Banach space ⋮ Characterization of optimal decompositions in real interpolation. II ⋮ On subdifferential calculus for set-valued mappings and optimality conditions ⋮ Alternating proximal algorithms for linearly constrained variational inequalities: application to domain decomposition for PDE's ⋮ On economic equilibrium type problems with applications ⋮ Fenchel duality in infinite-dimensional setting and its applications. ⋮ Unnamed Item ⋮ Projection and proximal point methods: Convergence results and counterexamples. ⋮ Wasserstein barycenters in the manifold of all positive definite matrices ⋮ Natural closures, natural compositions and natural sums of monotone operators ⋮ Higher-order total variation approaches and generalisations ⋮ Subdifferential calculus for set-valued mappings and optimality conditions for multiobjective optimization problems ⋮ Persistence and stability of solutions of Hamilton-Jacobi equations ⋮ \(\varepsilon \)-subdifferential as an enlargement of the subdifferential ⋮ Visco-penalization of the sum of two monotone operators ⋮ Subdifferentiability of infimal convolution on Banach couples ⋮ On functionals with convex Carathéodory integrands with a linear growth condition ⋮ Variational geometric approach to generalized differential and conjugate calculi in convex analysis ⋮ Revisiting some rules of convex analysis ⋮ On epsilon-stability in optimization ⋮ On the necessity of the Moreau-Rockafellar-Robinson qualification condition in Banach spaces ⋮ Unified models for second-order TV-type regularisation in imaging: a new perspective based on vector operators ⋮ Characterization of optimal decompositions in real interpolation ⋮ Properties of \(L^{1}-TGV^{2}\) : The one-dimensional case ⋮ Non-convex self-dual Lagrangians: new variational principles of symmetric boundary value problems ⋮ On the dependence of the solutions and optimal solutions of control problems on the control constraint set ⋮ Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming ⋮ A weaker regularity condition for subdifferential calculus and Fenchel duality in infinite dimensional spaces. ⋮ The asymptotic behavior of the composition of two resolvents ⋮ Necessary and sufficient conditions for stable conjugate duality ⋮ Characterizations of solution sets of convex vector minimization problems ⋮ A TGV-Based Framework for Variational Image Decompression, Zooming, and Reconstruction. Part I: Analytics ⋮ A TGV-Based Framework for Variational Image Decompression, Zooming, and Reconstruction. Part II: Numerics ⋮ Duality and infinite dimensional optimization ⋮ Differential stability of convex optimization problems under weaker conditions ⋮ Lower CS-closed sets and functions ⋮ Infimal Convolution of Oscillation Total Generalized Variation for the Recovery of Images with Structured Texture ⋮ Conjugate functions and subdifferentials in nonnormed situations for operators with complete graphs ⋮ A new geometric condition for Fenchel's duality in infinite dimensional spaces ⋮ (\(\epsilon\)-)efficiency in difference vector optimization ⋮ A study of the one dimensional total generalised variation regularisation problem

This page was built for publication: