Nonlocal Basis Pursuit: Nonlocal Optimal Design of Conductive Domains in the Vanishing Material Limit

DOI10.1137/22m1479166zbMath1518.49005arXiv2107.12994OpenAlexW3184460976MaRDI QIDQ6172784

José Carlos Bellido, Anton Evgrafov

Publication date: 20 July 2023

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2107.12994

zbMATH Keywords

Fenchel dualitynonlocal diffusioncontrol in the coefficientsbiting convergenceLebesgue spaces with mixed exponents

Mathematics Subject Classification ID

Convex programming (90C25) Design techniques (robust design, computer-aided design, etc.) (93B51) Existence of solutions for minimax problems (49J35) Methods involving semicontinuity and convergence; relaxation (49J45) Optimization problems in thermodynamics and heat transfer (80M50) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (2)

The dual approach to optimal control in the coefficients of nonlocal nonlinear diffusion ⋮ The Nonlocal Kelvin Principle and the Dual Approach to Nonlocal Control in the Conduction Coefficients

Cites Work

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• Solving semidefinite-quadratic-linear programs using SDPT3
• A new approach to Sobolev spaces and connections to \(\Gamma\)-convergence
• On the convergence of a class of nonlocal elliptic equations and related optimal design problems
• The spaces \(L^ p\), with mixed norm
• Optimal design problems governed by the nonlocal \(p\)-Laplacian equation
• Functional analysis, Sobolev spaces and partial differential equations
• Hencky-Prandtl nets and constrained Michell trusses
• An estimate in the spirit of Poincaré's inequality
• Variational methods for structural optimization
• Michell trusses in two dimensions as a \(\Gamma \)-limit of optimal design problems in linear elasticity
• A first-order primal-dual algorithm for convex problems with applications to imaging
• Optimal design versus maximal Monge-Kantorovich metrics
• Approximation of Lipschitz functions preserving boundary values
• Nonlocal optimal design: a new perspective about the approximation of solutions in optimal design
• Techniques of variational analysis
• Shape optimization of light structures and the vanishing mass conjecture
• MICHELL TRUSSES AND LINES OF PRINCIPAL ACTION
• Finite Element Methods for Navier-Stokes Equations
• Linear Inversion of Band-Limited Reflection Seismograms
• Remarks on Chacon's Biting Lemma
• Nonlocal Control in the Conduction Coefficients: Well-Posedness and Convergence to the Local Limit
• Existence and approximation of nonlocal optimal design problems driven by parabolic equations
• A Type of Nonlocal Elliptic Problem: Existence and Approximation Through a Galerkin--Fourier Method
• An Example of a Max-Min Problem in Partial Differential Equations
• Characterization of optimal shapes and masses through Monge-Kantorovich equation
• Shape optimization by the homogenization method

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