Exact penalty functions in single-stage stochastic programming¹

¹Research supported in part by a grant from Ruhrgas.

Abstract

We consider convex, stochastic programs involving no sequential decision making. It is shown that constraint qualifications of standard type ensure the existence of exact penalty functions. If data are also concave with respect to random parameters whose joint distribution majorities a scaled version of the uniform measure, then a particular penalty function is brought to the fore which is likely to be of practical interest,Its attraction comes mainly from the relative ease with which one can determine the size of an appropriate penalty parameter.

Keywords:

• Exact penalty functions
• stochastic programming
• convex analysis
• nonsmooth analysis
• constraint qualifications

AMS 1980 Subject Classifications:

• Primary: 90 C 15
• Secondary: 90 C 25

¹Research supported in part by a grant from Ruhrgas.

¹Research supported in part by a grant from Ruhrgas.

Notes

¹Research supported in part by a grant from Ruhrgas.