On relations between chance constrained and penalty function problems under discrete distributions

Abstract

We extend the theory of penalty functions to stochastic programming problems with nonlinear inequality constraints dependent on a random vector with known distribution. We show that the problems with penalty objective, penalty constraints and chance constraints are asymptotically equivalent under discretely distributed random parts.

We propose bounds on optimal values and convergence of optimal solutions. Moreover, we apply exact penalization under modified calmness property to improve the results.

Keywords

• Penalty functions
• Chance constraints
• Asymptotic equivalence
• Discrete distribution
• Exact penalization
• Calmness