Importance Sampling for Chance Constrained Optimization
Chance constrained problem is stated as minimizing a objective over solutions satisfying, with a given close to one probability, a system of convex constraints. These problems appears in many flavours of engineering. Probabilistic constraints, which appears at chance constrained problems, are not convex in general case. One of the main approach of solving these problems is to approximate the feasible set. Several state-of-the-art convex approximations are known: Markov, Chebyshev, Bernstein and sample average approximation (SAA). Moreover, we have the scenario approximation, which consists in sampling random points according to the nominal noise distribution and solving a deterministic problem afterwards. It is known to be one of the most accurate but time demanding approximation. Our goal is to propose a new way to reduce complexity of scenario approximation method for a linear objective and linear chance constraints with Gaussian noise by utilizing importance sampling.