Primal interior-point decomposition algorithms for two-stage stochastic extended second-order cone programming

ABSTRACT

We study and solve the two-stage stochastic extended second-order cone programming problem. We show that the barrier recourse functions and the composite barrier functions for this optimization problem are self-concordant families with respect to barrier parameters. These results are used to develop primal decomposition-based interior-point algorithms. The worst case iteration complexity of the developed algorithms is shown to be the same as that for the short- and long-step primal interior algorithms applied to the extensive formulation of our problem.

KEYWORDS:

• Extended second order cone
• conic programming
• stochastic programming
• interior-point algorithms
• self-concordance

AMS CLASSIFICATIONS:

• 90C15
• 90C22
• 90C30
• 90C51

Acknowledgements

A part of the author's work was performed while he was visiting Rochester Institute of Technology. The author thanks the anonymous referees for their valuable suggestions, their constructive comments have greatly enhanced the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of the author was supported in part by the Deanship of Scientific Research at the University of Jordan.