An inexact lagrange-newton method for stochastic quadratic programs with recourse
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In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered. By Monte Carlo simulation-based approximations of the objective function and its first (second) derivative, an inexact Lagrange-Newton type method is proposed. It is showed that this method is globally convergent with probability one. In particular, the convergence is local superlinear under an integral approximation error bound condition. Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
MR Subject Classification90C15 90C30 82B80
KeywordsLagrange-Newton method stochastic quadratic programming Monte Carlo simulation
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- 7.Rockafellar, R. T., Wets, R. J-B., A dual solution procedure for quadratic stochastic programs with simple recourse, in: A. Reinoza, ed., Numerical Methods, Lecture Notes in Mathematics, 1005, Berlin: Springer, 1983, 252–265.Google Scholar
- 9.Rockafellar, R. T., Wets, R. J-B., Linear-quadratic problems with stochastic optimization, Lecture Notes in Control and Information science, 81, Berlin: Springer, 1987, 545–560.Google Scholar
- 12.Birge, J. R., Chen Xiaojun, Qi Liqun, A stochastic Newton method for stochastic quadratic programs with recourse, Applied Mathematics Report, 94/9, School of Mathematics, Univ. of New South Wales, Sydney, 1994.Google Scholar