Optimization Problems With Concentration And Oscillation Effects: Relaxation Theory And Numerical Approximation

DOI10.1080/01630569908816908zbMath0940.49002OpenAlexW1987063601MaRDI QIDQ4265779

Martin Kružík, Tomáš Roubíček

Publication date: 23 November 1999

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569908816908

zbMATH Keywords

optimal controlYoung measuresrelaxationimpulsive controlDiPerna-Majda measures

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Existence theories for optimal control problems involving ordinary differential equations (49J15) Impulsive optimal control problems (49N25)

Related Items (13)

Semi-definite relaxations for optimal control problems with oscillation and concentration effects ⋮ Generalized $W^{1,1}$-Young Measures and Relaxation of Problems with Linear Growth ⋮ Sequential weak continuity of null Lagrangians at the boundary ⋮ Optimal control problems with oscillations, concentrations and discontinuities ⋮ Oscillations and concentrations generated by ${\mathcal A}$-free mappings and weak lower semicontinuity of integral functionals ⋮ On convergence of gradient-dependent integrands. ⋮ Optimal laminates in single-slip elastoplasticity ⋮ Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities ⋮ Oscillations and concentrations in sequences of gradients ⋮ A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures ⋮ A sequential quadratic Hamiltonian scheme to compute optimal relaxed controls ⋮ Modelling of Thin Martensitic Films with Nonpolynomial Stored Energies ⋮ Convergence of adaptive finite element methods for a nonconvex double-well minimization problem

Cites Work

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• Parametrized measures and variational principles
• Impulsive control and optimization
• Explicit characterization of \(L^ p\)-Young measures
• Convergence of solution to nonlinear dispersive equations
• New Existence Results for Optimal Controls in the Absence of Convexity: The Importance of Extremality
• Numerical approximation of parametrized measures
• The Generalized Solutions of Nonlinear Optimization Problems with Impulse Control

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