Convex Relaxations of Integral Variational Problems: Pointwise Dual Relaxation and Sum-of-Squares Optimization

DOI10.1137/21m1455127zbMath1515.49009arXiv2110.03079OpenAlexW3203691100MaRDI QIDQ6155878

Giovanni Fantuzzi, Jason J. Bramburger, Alexander Chernyavsky, David Goluskin

Publication date: 7 June 2023

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

Full work available at URL: https://arxiv.org/abs/2110.03079

zbMATH Keywords

calculus of variationsconvex relaxationpolynomial optimizationsum-of-squares programming

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Polynomial optimization (90C23)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dissipation inequalities for the analysis of a class of PDEs
• Physical interpretation and strengthening of M.H. Protter's method for vibrating nonhomogeneous membranes; its analogue for Schrödinger's equation
• Parametrized measures and variational principles
• Domain perturbations and estimates for the solutions of second order elliptic equations.
• Semidefinite programming relaxations for semialgebraic problems
• Safety verification for distributed parameter systems using barrier functionals
• From a nonlinear, nonconvex variational problem to a linear, convex formulation
• An exact Jacobian SDP relaxation for polynomial optimization
• Explicit solutions of nonconvex variational problems in dimension one
• A moment approach for entropy solutions to nonlinear hyperbolic PDEs
• The null set of the Euler-Lagrange operator
• Matrix sum-of-squares relaxations for robust semi-definite programs
• Global Optimization with Polynomials and the Problem of Moments
• Latest Developments in the SDPA Family for Solving Large-Scale SDPs
• An Introduction to Polynomial and Semi-Algebraic Optimization
• Polynomial sum of squares in fluid dynamics: a review with a look ahead
• Stability Analysis for a Class of Partial Differential Equations via Semidefinite Programming
• On the Equation div( | ∇u | p-2 ∇u) + λ | u | p-2 u = 0
• Optimal use of the translation method and relaxations of variational problems
• Eigenvalues of Elliptic Boundary Value Problems With an Indefinite Weight Function
• Some NP-complete problems in quadratic and nonlinear programming
• Approximation of domains with Lipschitzian boundary
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming
• Optimal control of linear PDEs using occupation measures and SDP relaxations
• Pre- and Post-Processing Sum-of-Squares Programs in Practice
• EIGENVALUES OF THE FINSLER p ‐LAPLACIAN ON VARYING DOMAINS
• A framework for input–output analysis of wall-bounded shear flows
• Direct methods in the calculus of variations

This page was built for publication: Convex Relaxations of Integral Variational Problems: Pointwise Dual Relaxation and Sum-of-Squares Optimization