TY - CHAP

T1 - The homogeneous self-dual method

AU - Vanderbei, Robert J.

N1 - Publisher Copyright:
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020.

PY - 2020

Y1 - 2020

N2 - In Chapter 18, we described and analyzed an interior-point method called the path-following algorithm. This algorithm is essentially what one implements in practice but as we saw in the section on convergence analysis, it is not easy (and perhaps not possible) to give a complete proof that the method converges to an optimal solution. If convergence were completely established, the question would still remain as to how fast is the convergence. In this chapter, we shall present a similar algorithm for which a complete convergence analysis can be given.

AB - In Chapter 18, we described and analyzed an interior-point method called the path-following algorithm. This algorithm is essentially what one implements in practice but as we saw in the section on convergence analysis, it is not easy (and perhaps not possible) to give a complete proof that the method converges to an optimal solution. If convergence were completely established, the question would still remain as to how fast is the convergence. In this chapter, we shall present a similar algorithm for which a complete convergence analysis can be given.

UR - http://www.scopus.com/inward/record.url?scp=85090007620&partnerID=8YFLogxK

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U2 - 10.1007/978-3-030-39415-8_22

DO - 10.1007/978-3-030-39415-8_22

M3 - Chapter

AN - SCOPUS:85090007620

T3 - International Series in Operations Research and Management Science

SP - 365

EP - 385

BT - International Series in Operations Research and Management Science

PB - Springer

ER -