A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs

We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on bi-objective viewpoint programs that seeks solutions optimal objective value versus risk constraints violation. To this end, we construct reformulated problem whose to minimize probability violation subject deterministic convex (which includes bound function value). adapt existing smoothing-based approaches problems derive convergent sequence smooth approximations our problem, and apply projected subgradient algorithm solve it. In contrast with exterior sampling-based (such as sample average approximation) approximate original program one having finite support, proposal converges stationary thereby avoiding poor local may be an artefact fixed sample. also tailored implementation chooses key algorithmic parameters data. Computational results four test from literature indicate proposed can efficiently determine good frontier.