  We study the problem of designing systems in order to minimize cost while
meeting a given flexibility target. Flexibility is attained by enforcing a
joint chance constraint, which ensures that the system will exhibit feasible
operation with a given target probability level. Unfortunately, joint chance
constraints are complicated mathematical objects that often need to be
reformulated using mixed-integer programming (MIP) techniques. In this work, we
cast the design problem as a conflict resolution problem that seeks to minimize
cost while maximizing flexibility. We propose a purely continuous relaxation of
this problem that provides a significantly more scalable approach relative to
MIP methods and show that the formulation delivers solutions that closely
approximate the Pareto set of the original joint chance-constrained problem.

Optimization and Control