Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization | Paper Citation Record

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This paper cites A review of the design methods of complex topology structures for 3D printing.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A review of the design methods of complex topology structures for 3D printing

Reference 1

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This paper cites Topology Optimization of Continuum Structures: A Review.Applied Mechanics Reviews.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Topology Optimization of Continuum Structures: A Review.Applied Mechanics Reviews

Reference 2

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This paper cites A review about the engineering design of optimal heat transfer systems using topology optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A review about the engineering design of optimal heat transfer systems using topology optimization

Reference 3

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This paper cites A Review of Topology Optimisation for Fluid-Based Problems.Fluids.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A Review of Topology Optimisation for Fluid-Based Problems.Fluids

Reference 4

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This paper cites The method of moving asymptotes—a new method for structural optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization The method of moving asymptotes—a new method for structural optimization

Reference 5

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This paper cites An SLP algorithm and its application to topology optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization An SLP algorithm and its application to topology optimization

Reference 6

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This paper cites An efficient second-order SQP method for structural topology optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization An efficient second-order SQP method for structural topology optimization

Reference 7

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.636914Z

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This paper cites A review of homogenization and topology optimization III—topology optimization using optimality criteria.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A review of homogenization and topology optimization III—topology optimization using optimality criteria

Reference 8

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.622905Z

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This paper cites Primal-dual Newton-type interior-point method for topology optimization.Journal of Optimization Theory and Applications.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Primal-dual Newton-type interior-point method for topology optimization.Journal of Optimization Theory and Applications

Reference 9

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This paper cites Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method

Reference 10

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.594915Z

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This paper cites Inertial projected gradient method for large-scale topology optimization.Japan Journal of Industrial and Applied Mathematics.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Inertial projected gradient method for large-scale topology optimization.Japan Journal of Industrial and Applied Mathematics

Reference 11

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.581023Z

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This paper cites Parameter-free projected gradient descent.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Parameter-free projected gradient descent

Reference 12

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This paper cites Boosting the robustness of neural networks with M-PGD.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Boosting the robustness of neural networks with M-PGD

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.153675Z

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This paper cites A random active set method for strictly convex quadratic problem with simple bounds.Mathematics of Computation.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A random active set method for strictly convex quadratic problem with simple bounds.Mathematics of Computation

Reference 14

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.567182Z

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This paper cites Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination.Computational Optimization and Applications.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Minimizing quadratic functions subject to bound constraints with the rate of convergence and finite termination.Computational Optimization and Applications

Reference 15

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.553073Z

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Observation bdbf7fe8-b4cf-434d-b9a4-18d7f885cddf · outbound

This paper cites An infeasible active set method for quadratic problems with simple bounds.SIAM Journal on Optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization An infeasible active set method for quadratic problems with simple bounds.SIAM Journal on Optimization

Reference 16

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.539005Z

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This paper cites A feasible active set method for strictly convex quadratic problems with simple bounds.SIAM Journal on Optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A feasible active set method for strictly convex quadratic problems with simple bounds.SIAM Journal on Optimization

Reference 17

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.525182Z

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This paper cites Primal and dual active-set methods for convex quadratic programming.Mathematical Programming.2016;159(1):469–.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Primal and dual active-set methods for convex quadratic programming.Mathematical Programming.2016;159(1):469–

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.139547Z

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This paper cites An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints

Reference 19

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.498879Z

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This paper cites A two-stage active-set algorithm for bound-constrained optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A two-stage active-set algorithm for bound-constrained optimization

Reference 20

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.483949Z

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Observation 62b3f21e-1cbb-4250-8cca-e5e1c2dd0f94 · outbound

This paper cites Topology optimization for additive manufacturing: considering maximum overhang constraint.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Topology optimization for additive manufacturing: considering maximum overhang constraint

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.125332Z

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This paper cites Undercut and overhang angle control in topology optimization: A density gradient based integral approach.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Undercut and overhang angle control in topology optimization: A density gradient based integral approach

Reference 22

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.469906Z

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Observation 2d287ef2-a86a-4502-9d54-9de569630ef9 · outbound

This paper cites Additively manufactured conformal cooling channels through topology optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Additively manufactured conformal cooling channels through topology optimization

Reference 23

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.455770Z

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Observation ac5c4e04-01fd-4185-94a9-20cbf8e2ee87 · outbound

This paper cites Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design

Reference 24

Resolution: verified exact; doi, observed 2026-08-11T18:42:34.111509Z

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This paper cites First-order methods in optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization First-order methods in optimization

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.097446Z

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This paper cites Improved analysis of clipping algorithms for non-convex optimization.Advances in Neural Information Processing Systems.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Improved analysis of clipping algorithms for non-convex optimization.Advances in Neural Information Processing Systems

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.083328Z

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This paper cites QPSchur: a dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization QPSchur: a dual, active-set, Schur-complement method for large-scale and structured convex quadratic programming

Reference 27

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.440926Z

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This paper cites Active-set methods for quadratic programming.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Active-set methods for quadratic programming

Reference 28

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Observation c47c4d9d-27c2-48d4-ac1a-0b7a174ed82f · outbound

This paper cites DFEMwork: A Parallel Computing Framework for Material Processing.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization DFEMwork: A Parallel Computing Framework for Material Processing

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.054862Z

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Observation 018a98cc-563f-4b83-a5bf-713b9f8c59e6 · outbound

This paper cites Development of a Topology Optimization Framework For Cooling Channel Design in Die Casting Molds.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Development of a Topology Optimization Framework For Cooling Channel Design in Die Casting Molds

Reference 30

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This paper cites A Projected Gradient and Constraint Linearization Method for Nonlinear Model Predictive Control.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization A Projected Gradient and Constraint Linearization Method for Nonlinear Model Predictive Control

Reference 31

Resolution: verified exact; doi, observed 2026-08-11T18:42:33.426520Z

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Observation 7097c25e-3c9a-4667-85ef-ee645f877f59 · outbound

This paper cites Constrained optimization and Lagrange multiplier methods.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Constrained optimization and Lagrange multiplier methods

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:34.025511Z

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This paper cites Numerical optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Numerical optimization

Reference 33

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This paper cites Linear Algebra and Its Applications.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Linear Algebra and Its Applications

Reference 34

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This paper cites Convex Optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Convex Optimization

Reference 35

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This paper cites dSJ, et al.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization dSJ, et al

Reference 36

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This paper cites Thermofluid Topology Optimization for Cooling Channel Design.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Thermofluid Topology Optimization for Cooling Channel Design

Reference 37

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Observation 4a45d354-9f98-4ea4-b448-c4d9e317431d · outbound

This paper cites Filters in Topology Optimization Based on Helmholtz-type Differential Equations.International Journal for Numerical Methods in Engineering.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Filters in Topology Optimization Based on Helmholtz-type Differential Equations.International Journal for Numerical Methods in Engineering

Reference 38

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This paper cites On projection methods, convergence and robust formulations in topology optimization.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization On projection methods, convergence and robust formulations in topology optimization

Reference 39

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This paper cites Generating optimal topologies in structural design using a homogenization method.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Generating optimal topologies in structural design using a homogenization method

Reference 40

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This paper cites Volume 11: Heat Transfer and Thermal Engineering of ASME International Mechanical Engineering Congress and Exposition; : 2021.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Volume 11: Heat Transfer and Thermal Engineering of ASME International Mechanical Engineering Congress and Exposition; : 2021

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:33.967424Z

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Observation 4141ba06-c179-4706-8624-8001bd22b804 · outbound

This paper cites Gmsh.; 2020.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Gmsh.; 2020

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:33.953355Z

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This paper cites The NLopt Nonlinear-Optimization Package.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization The NLopt Nonlinear-Optimization Package

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:42:33.939429Z

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This paper cites Attacking Large Language Models with Projected Gradient Descent.

Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Attacking Large Language Models with Projected Gradient Descent

Reference 44

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Improving the Robustness of the Projected Gradient Descent Method for Nonlinear Constrained Optimization Problems in Topology Optimization Unresolved cited work

Reference 508

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