Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/330542 
Year of Publication: 
2025
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 93 [Issue:] 1 [Publisher:] Springer US [Place:] New York, NY [Year:] 2025 [Pages:] 299-333
Publisher: 
Springer US, New York, NY
Abstract: 
Linear-parametric optimization, where multiple objectives are combined into a single objective using linear combinations with parameters as coefficients, has numerous links to other fields in optimization and a wide range of application areas. In this survey, we provide a comprehensive overview of structural results and algorithmic strategies for solving linear-parametric optimization problems exactly and approximately. Transferring concepts from related areas such as multi-objective optimization provides further relevant results. The survey consists of two parts: First, we list strategies that work in a general fashion and do not rely on specific problem structures. Second, we look at well-studied parametric optimization problems and cover both important theoretical results and specialized algorithmic approaches for these problems. Among these problems are parametric variants of shortest path problems, minimum cost flow and maximum flow problems, spanning tree problems, the knapsack problem, and matching problems. Overall, we cover the results from 128 publications (and refer to 35 supplemental works) published between 1963 and 2024.
Subjects: 
Parametric optimization
Parametric programming
Approximation algorithms
Combinatorial optimization
Survey
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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