Generalized Second Derivatives of Convex Functions and Saddle Functions
From MaRDI portal
Publication:3196894
DOI10.2307/2001522zbMath0712.49011OpenAlexW4245876463MaRDI QIDQ3196894
Publication date: 1990
Full work available at URL: https://doi.org/10.2307/2001522
sensitivity analysissubgradientsaddle functionsepi-hypo-differentiabilityproto-differentiationsecond-order epi-derivatives
Convex programming (90C25) Variational inequalities (49J40) Nonsmooth analysis (49J52) Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Set-valued and function-space-valued mappings on manifolds (58C06)
Related Items
Second-order subgradients of convex integral functionals, Graphical methods in first and second-order differentiability theory of integral functionals, Proto-derivative formulas for basic subgradient mappings in mathematical programming, A set-valued analysis approach to second order differentiation of nonsmooth functions, Convergence results for a self-dual regularization of convex problems, Variational Analysis of Composite Models with Applications to Continuous Optimization, Second-order subdifferentials of \(C^{1,1}\) functions and optimality conditions, Proto-differentiability of set-valued mappings and its applications in optimization, Second order epi derivatives and the Dupin indicatrix for nonsmooth functions, Second-order normal vectors to a convex epigraph, The landscape of the proximal point method for nonconvex-nonconcave minimax optimization, Role of subgradients in variational analysis of polyhedral functions, On second-order directional derivatives, A Chain Rule for Strict Twice Epi-Differentiability and Its Applications, Twice Epi-Differentiability of Extended-Real-Valued Functions with Applications in Composite Optimization, Unnamed Item, Local second-order approximations and applications in optimization, Prox-regular functions in variational analysis, Complément de Schur et sous-différentiel du second ordre d'une fonction convexe, Sensitivity analysis of maximally monotone inclusions via the proto-differentiability of the resolvent operator, Second-order conditions for existence of augmented Lagrange multipliers for eigenvalue composite optimization problems, On the convergence of subdifferentials of convex functions, Second Order Differentiability of Convex Functions in Banach Spaces, Sensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity Operator, Constrained control problems with convex cost in Hilbert space, Epi-Derivatives of Integral Functionals with Applications, Generalized Second-Order Derivatives of Convex Functions in Reflexive Banach Spaces, The 𝒰-Lagrangian of a convex function, Differential sensitivity analysis of variational inequalities with locally Lipschitz continuous solution operators, First- and second-order epi-differentiability in eigenvalue optimization, Sensitivity analysis of a Tresca-Type Problem leads to Signorini’s conditions, Augmented Lagrangian duality for composite optimization problems, Limiting behavior of the approximate second-order subdifferential of a convex function
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Approximate first-order and second-order directional derivatives of a marginal function in convex optimization
- Technical note: Directional derivatives in nonsmooth optimization
- Generalized Hessian matrix and second-order optimality conditions for problems with \(C^{1,1}\) data
- Maximal monotone relations and the second derivatives of nonsmooth functions
- Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton
- Convergence of convex-concave saddle functions: Applications to convex programming and mechanics
- Proto-differentiability of set-valued mappings and its applications in optimization
- Convergence of convex sets and of solutions of variational inequalities
- A Convergence Theory for Saddle Functions
- A Generalized Second-Order Derivative in Nonsmooth Optimization
- Calculus Rules on the Approximate Second-Order Directional Derivative of a Convex Function
- Limiting behaviour of the approximate first order and second order directional derivatives for a convex function
- Stability in Mathematical Programming with Nondifferentiable Data
- Lipschitz Behavior of Solutions to Convex Minimization Problems
- Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives
- Calculus rules on a new set—valued second order derivative for convex functions
- Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs
- Optimization and nonsmooth analysis
- Second-Order Necessary Conditions in Constrained Semismooth Optimization
- Sensitivity Analysis of Nonlinear Programs and Differentiability Properties of Metric Projections
- Second Order Directional Derivatives in Parametric Optimization Problems
- First- and Second-Order Epi-Differentiability in Nonlinear Programming
- Second-Order Sufficient Conditions in Nonsmooth Optimization
- On the Convergence of Sequences of Convex Sets in Finite Dimensions
- Generalized Directional Derivatives and Subgradients of Nonconvex Functions
- A unified theory of first and second order conditions for extremum problems in topological vector spaces
- Generalized Gradients and Applications
- On second derivates of convex functions.
- On Sufficient Conditions in Nonsmooth Optimization
- A General Sufficiency Theorem for Nonsmooth Nonlinear Programming
- On the differential properties of the support function of the∈-subdifferential of a convex function
- Approximating a Second-Order Directional Derivative for Nonsmooth Convex Functions
- On second-order directional derivatives
- Minimax Theorems and Conjugate Saddle-Functions.
- Convergence of Sequences of Convex Sets, Cones and Functions. II
- Convex Analysis
- Convergence of sequences of convex sets, cones and functions