Regularity Conditions for a Class of Convex Programs

This paper develops regularity conditions for a class of convex programming problems (convex objective functions and linear constraints). The objective functions considered are lower semicontinuous and have bounded level sets. The constraint set may be unbounded. Results pertaining to the solvability, stability and dualizability of such programs are obtained. The results are then applied to a class of nonlinear stochastic programs with recourse.