Gradient-Based Solution Algorithms for a Class of Bilevel Optimization and Optimal Control Problems with a Nonsmooth Lower Level
From MaRDI portal
Publication:5211812
DOI10.1137/18M1225707zbMath1432.49007WikidataQ126304153 ScholiaQ126304153MaRDI QIDQ5211812
Publication date: 28 January 2020
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
total variationoptimal controlnonsmooth optimizationparameter identificationmachine learningbilevel optimizationCasson fluidelliptic variational inequality of the second kind
Computing methodologies for image processing (68U10) Variational inequalities (49J40) Nonsmooth analysis (49J52) Non-Newtonian fluids (76A05) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Inverse problems in optimal control (49N45)
Related Items (4)
On the identification and optimization of nonsmooth superposition operators in semilinear elliptic PDEs ⋮ A Nonsmooth Trust-Region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities ⋮ A note on a bilevel problem for parameter learning for inverse problems with the wave equation ⋮ Bilevel Methods for Image Reconstruction
Uses Software
Cites Work
- Bilevel optimization for calibrating point spread functions in blind deconvolution
- A natural nonconforming FEM for the Bingham flow problem is quasi-optimal
- Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the second kind
- Solving semi-infinite programs by smoothing projected gradient method
- Bilevel parameter learning for higher-order total variation regularisation models
- Optimization of mixed variational inequalities arising in flow of viscoplastic materials
- On the numerical simulation of Bingham viscoplastic flow: old and new results
- Conjugate gradient algorithms in nonconvex optimization
- Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel-Bulkley fluids
- Stability for the solutions of \(div(| \nabla u| ^{p-2}\nabla u)=f\) with varying p
- Lectures on numerical methods for non-linear variational problems
- Descent approaches for quadratic bilevel programming
- Foundations of bilevel programming
- \(L^\infty\)-error estimates for the obstacle problem revisited
- Optimal selection of the regularization function in a weighted total variation model. I: Modelling and theory
- Optimal selection of the regularization function in a weighted total variation model. II: Algorithm, its analysis and numerical tests
- Optimal control of a non-smooth semilinear elliptic equation
- Implicit multifunction theorems for the sensitivity analysis of variational conditions
- The bilevel programming problem: reformulations, constraint qualifications and optimality conditions
- Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints
- Differential sensitivity analysis of variational inequalities with locally Lipschitz continuous solution operators
- Sensitivity analysis for a class of \(H_{0}^{1}\)-elliptic variational inequalities of the second kind
- On the directional differentiability of the solution mapping for a class of variational inequalities of the second kind
- On solving simple bilevel programs with a nonconvex lower level program
- Convergence of algorithms for perturbed optimization problems
- Analysis of Inexact Trust-Region SQP Algorithms
- Bilevel Optimal Control Problems with Pure State Constraints and Finite-dimensional Lower Level
- Weak and strong stationarity in generalized bilevel programming and bilevel optimal control
- A Bilevel Optimization Approach for Parameter Learning in Variational Models
- Variational Analysis in Sobolev and BV Spaces
- Introduction to Nonlinear Optimization
- Robust Sparse Analysis Regularization
- New Necessary Optimality Conditions for Bilevel Programs by Combining the MPEC and Value Function Approaches
- Optimal Control of a Class of Variational Inequalities of the Second Kind
- Bilevel Optimization with Nonsmooth Lower Level Problems
- Optimization—Theory and Practice
- A necessary and a sufficient optimality condition for bilevel programming problems
- Variational Analysis
- Necessary Optimality Conditions for Optimization Problems with Variational Inequality Constraints
- Nichtlineare Funktionalanalysis
- Trust Region Methods
- Bilevel approaches for learning of variational imaging models
- Necessary optimality conditions for a special class of bilevel programming problems with unique lower level solution
- A bilevel approach for parameter learning in inverse problems
- Global Convergence of a Class of Trust Region Algorithms for Optimization Using Inexact Projections on Convex Constraints
- Optimality conditions for bilevel programming problems
- A Nonsmooth Trust-Region Method for Locally Lipschitz Functions with Application to Optimization Problems Constrained by Variational Inequalities
- Bilevel Programming Problems
- KKT Reformulation and Necessary Conditions for Optimality in Nonsmooth Bilevel Optimization
- Regularization and Variable Selection Via the Elastic Net
- Learning optimal spatially-dependent regularization parameters in total variation image denoising
- Constraint Qualifications and KKT Conditions for Bilevel Programming Problems
- New necessary optimality conditions in optimistic bilevel programming
- Variational methods in the theory of the fluidity of a viscous-plastic medium
- On stagnant flow regions of a viscous-plastic medium in pipes
- On qualitative singularities of the flow of a viscoplastic medium in pipes
- Sensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity Operator
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Gradient-Based Solution Algorithms for a Class of Bilevel Optimization and Optimal Control Problems with a Nonsmooth Lower Level
