An Inexact Bundle Algorithm for Nonconvex Nonsmooth Minimization in Hilbert Space

DOI10.1137/18M1221849zbMath1461.49041OpenAlexW2973491413WikidataQ127228590 ScholiaQ127228590MaRDI QIDQ5193505

Michael Ulbrich, Lukas Hertlein

Publication date: 20 September 2019

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/18m1221849

zbMATH Keywords

nonsmooth optimizationerror estimatesnonconvex bundle methodinexact function valuesinexact subgradientsoptimal control of obstacle problem

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Nonconvex programming, global optimization (90C26) Derivative-free methods and methods using generalized derivatives (90C56) Optimality conditions for problems involving partial differential equations (49K20) Nonsmooth analysis (49J52) Numerical methods based on nonlinear programming (49M37)

Related Items

Challenges in optimization with complex PDE-systems. Abstracts from the workshop held February 14--20, 2021 (hybrid meeting), An Inexact Bundle Method and Subgradient Computations for Optimal Control of Deterministic and Stochastic Obstacle Problems, An Approximation Scheme for Distributionally Robust PDE-Constrained Optimization, Adaptive Bundle Methods for Nonlinear Robust Optimization, Semismoothness for Solution Operators of Obstacle-Type Variational Inequalities with Applications in Optimal Control, 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, On the Characterization of Generalized Derivatives for the Solution Operator of the Bilateral Obstacle Problem, Computation of a Bouligand Generalized Derivative for the Solution Operator of the Obstacle Problem, Nonsmooth optimization by successive abs-linearization in function spaces

Uses Software

• PNEW

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonsmooth bundle trust-region algorithm with applications to robust stability
• Convex proximal bundle methods in depth: a unified analysis for inexact oracles
• On approximations with finite precision in bundle methods for nonsmooth optimization
• Globally convergent limited memory bundle method for large-scale nonsmooth optimization
• A bundle-Newton method for nonsmooth unconstrained minimization
• Convergence of some algorithms for convex minimization
• Approximate convexity and submonotonicity.
• Non-smooth optimization for robust control of infinite-dimensional systems
• Approximations in proximal bundle methods and decomposition of convex programs
• Methods of descent for nondifferentiable optimization
• A strongly convergent proximal bundle method for convex minimization in Hilbert spaces
• A Redistributed Proximal Bundle Method for Nonconvex Optimization
• Limited memory bundle method for large bound constrained nonsmooth optimization: convergence analysis
• A Linearization Algorithm for Nonsmooth Minimization
• A Dual Method for Certain Positive Semidefinite Quadratic Programming Problems
• Error Estimates for the Approximation of a Class of Variational Inequalities
• Semismooth and Semiconvex Functions in Constrained Optimization
• An Introduction to Variational Inequalities and Their Applications
• Restricted Step and Levenberg–Marquardt Techniques in Proximal Bundle Methods for Nonconvex Nondifferentiable Optimization
• A Priori Finite Element Error Analysis for Optimal Control of the Obstacle Problem
• The Mathematical Theory of Finite Element Methods
• A Proximal Bundle Method with Approximate Subgradient Linearizations
• Bundle Method for Non-Convex Minimization with Inexact Subgradients and Function Values
• Convex analysis and monotone operator theory in Hilbert spaces
• A proximal bundle method based on approximate subgradients
• A proximal bundle method for nonsmooth nonconvex functions with inexact information