Discrete approximation of linear two-stage stochastic programming problem. (English) Zbl 0587.90078

The author deals with the approximate solution of linear stochastic programming problems with complete recourse. He replaces the static form of the problem in function space by a sequence of discretized problems in finite-dimensional spaces. It is proved that a sequence of solutions of the discretized problems is weakly compact and that the optimal values of discrete problems converge to the initial one. The weak limit points of a sequence of solutions of the discrete problems are solutions of the initial problem. Under complementary conditions the convergence is strong.


90C15 Stochastic programming
65K05 Numerical mathematical programming methods
Full Text: DOI


[1] DOI: 10.1090/S0025-5718-1969-0247746-7
[2] DOI: 10.1287/mnsc.1.3-4.197 · Zbl 0995.90589
[3] DOI: 10.1007/BF01406972 · Zbl 0277.65043
[4] Olsen P., SIAM J. Control Optimiz 14 pp 528– · Zbl 0336.90041
[5] Stummel, P. 1972. Discrete convergence of mappings. Top. Numer. Anal. Proc. Conf. Numer. Analysis. 1972, Dublin. pp.285–310.
[6] DOI: 10.1016/0362-546X(78)90013-5 · Zbl 0401.65034
[7] DOI: 10.1007/BF00969138 · Zbl 0229.45013
[8] Vasin V. V., USSR Comput. Math. and Math. Physics 22 pp 824– (1982) · Zbl 0516.65044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.