A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design

DOI10.4208/aamm.oa-2022-0003OpenAlexW4366532007MaRDI QIDQ6188656

Jianxin Zhang, Jianhua Yuan, Mengyue Wu

Publication date: 11 January 2024

Published in: Advances in Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/aamm.oa-2022-0003

zbMATH Keywords

finite element methodlinear approximationfractional programmingPDE constrained optimizationphotonic band gap

Mathematics Subject Classification ID

Large-scale problems in mathematical programming (90C06) Nonconvex programming, global optimization (90C26) Numerical optimization and variational techniques (65K10) Linear programming (90C05) Numerical methods based on nonlinear programming (49M37)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Galerkin spectral approximation of elliptic optimal control problems with \(H^1\)-norm state constraint
• Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods
• Data assimilation in weather forecasting: a case study in PDE-constrained optimization
• A linear-time algorithm for the trust region subproblem based on hidden convexity
• An alternating direction method of multipliers for elliptic equation constrained optimization problem
• Numerical PDE-Constrained Optimization
• Error Analysis of a Mixed Finite Element Method for the Molecular Beam Epitaxy Model
• Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization
• Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell’s Equations
• Systematic design of phononic band–gap materials and structures by topology optimization
• Convergence Analysis and Error Estimate for Distributed Optimal Control Problems Governed by Stokes Equations with Velocity-Constraint
• A Weak Galerkin Mixed Finite Element Method for Acoustic Wave Equation
• Analysis of Finite Difference Approximations of an Optimal Control Problem in Economics
• Continuation Finite Element Simulation of Second Harmonic Generation in Photonic Crystals

This page was built for publication: A Convex Approximation for a PDE Constrained Fractional Optimization Problem with an Application to Photonic Crystal Design