Two wide neighborhood interior-point methods for symmetric cone optimization

M. Sayadi Shahraki (), H. Mansouri () and M. Zangiabadi ()
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M. Sayadi Shahraki: Institute for Research in Fundamental Sciences (IPM)
H. Mansouri: Shahrekord University
M. Zangiabadi: Shahrekord University

Computational Optimization and Applications, 2017, vol. 68, issue 1, No 2, 29-55

Abstract: Abstract In this paper, we present two primal–dual interior-point algorithms for symmetric cone optimization problems. The algorithms produce a sequence of iterates in the wide neighborhood $$\mathcal {N}(\tau ,\,\beta )$$ N ( τ , β ) of the central path. The convergence is shown for a commutative class of search directions, which includes the Nesterov–Todd direction and the xs and sx directions. We derive that these two path-following algorithms have $$\begin{aligned} \text{ O }\left( \sqrt{r\text{ cond }(G)}\log \varepsilon ^{-1}\right) , \text{ O }\left( \sqrt{r}\left( \text{ cond }(G)\right) ^{1/4}\log \varepsilon ^{-1}\right) \end{aligned}$$ O r cond ( G ) log ε - 1 , O r cond ( G ) 1 / 4 log ε - 1 iteration complexity bounds, respectively. The obtained complexity bounds are the best result in regard to the iteration complexity bound in the context of the path-following methods for symmetric cone optimization. Numerical results show that the algorithms are efficient for this kind of problems.

Keywords: Symmetric cone; Euclidean Jordan algebra; Wide neighborhood; Predictor–corrector interior-point method; 90C05; 90C51 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10589-017-9905-x

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