Tracing Locally Pareto-Optimal Points by Numerical Integration

DOI10.1137/20M1341106zbMath1477.90095arXiv2004.10820OpenAlexW3199726775MaRDI QIDQ3382784

Matthias Bolten, Onur Tanil Doganay, Hanno Gottschalk, Kathrin Klamroth

Publication date: 22 September 2021

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

Full work available at URL: https://arxiv.org/abs/2004.10820

zbMATH Keywords

scalarizationshape optimizationbiobjective optimizationPareto tracing

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Management decision making, including multiple objectives (90B50) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Optimization of shapes other than minimal surfaces (49Q10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Uses Software

• NBI

Cites Work

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• The weighted sum method for multi-objective optimization: new insights
• The normalized normal constraint method for generating the Pareto frontier
• Minimal failure probability for ceramic design via shape control
• Tracing the Pareto frontier in bi-objective optimization problems by ODE techniques
• Multiobjective search algorithm with subdivision technique
• On continuation methods for non-linear bi-objective optimization: towards a certified interval-based approach
• Nonlinear multiobjective optimization
• Nonlinear multiobjective optimization. A generalized homotopy approach
• Covering Pareto sets by multilevel subdivision techniques
• An analytical study in multi-physics and multi-criteria shape optimization
• Gradient based biobjective shape optimization to improve reliability and cost of ceramic components
• Shape gradients for the failure probability of a mechanic component under cyclic loading: a discrete adjoint approach
• An introduction to ordinary differential equations
• Approximation methods in multiobjective programming
• Solving Ordinary Differential Equations I
• Newton's Method for Multiobjective Optimization
• An Adaptive Scalarization Method in Multiobjective Optimization
• Introduction to Numerical Continuation Methods
• Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems
• Multicriteria Optimization
• Numerical Methods for Ordinary Differential Equations
• Numerical shape optimization to decrease failure probability of ceramic structures

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