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Primal-Dual Methods and Minimum Cost Flow

In: Introduction to Combinatorial Optimization

Author

Listed:
  • Ding-Zhu Du

    (University of Texas, Dallas)

  • Panos Pardalos

    (University of Florida)

  • Xiaodong Hu

    (Chinese Academy of Sciences)

  • Weili Wu

    (University of Texas at Dallas)

Abstract

There are three types of incremental methods, primal, dual, and primal-dual. In Chap. 6, we touched all of them for linear programming (LP). This chapter is contributed specially to primal-dual methods for further exploring techniques about primal-dual with a special interest in the minimum cost flow. Actually, the minimum cost flow is a fundamental optimization problem on networks. The shortest path problem and the assignment problem can be formulated as its special cases. We begin with the study of the assignment problem.

Suggested Citation

  • Ding-Zhu Du & Panos Pardalos & Xiaodong Hu & Weili Wu, 2022. "Primal-Dual Methods and Minimum Cost Flow," Springer Optimization and Its Applications, in: Introduction to Combinatorial Optimization, chapter 0, pages 175-198, Springer.
  • Handle: RePEc:spr:spochp:978-3-031-10596-8_7
    DOI: 10.1007/978-3-031-10596-8_7
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    Cited by:

    1. Yang, Kai & Hou, Lei & Man, Jianfeng & Yu, Qiaoyan & Li, Yu & Zhang, Xinru & Liu, Jiaquan, 2023. "Supply reliability analysis of natural gas pipeline network based on demand-side economic loss risk," Reliability Engineering and System Safety, Elsevier, vol. 230(C).

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