Quantitative stability of full random two-stage problems with quadratic recourse

ABSTRACT

In this paper, we discuss quantitative stability of two-stage stochastic programs with quadratic recourse where all parameters in the second-stage problem are random. By establishing the Lipschitz continuity of the feasible set mapping of the restricted Wolfe dual of the second-stage quadratic programming in terms of the Hausdorff distance, we prove the local Lipschitz continuity of the integrand of the objective function of the two-stage stochastic programming problem and then establish quantitative stability results of the optimal values and the optimal solution sets when the underlying probability distribution varies under the Fortet–Mourier metric. Finally, the obtained results are applied to study the asymptotic behaviour of the empirical approximation of the model.

KEYWORDS:

• Stochastic programming
• quadratic programming
• Fortet–Mourier metric
• asymptotic behaviour

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C15
• 90C31

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author was supported by the National Natural Science Foundation of China under Project No. 11801057 and the Fundamental Research Funds for the Central Universities under Project No. DUT17RC(3)058. The fourth author was supported by the National Natural Science Foundation of China under Project Nos. 11571059, 11731013 and 91330206.