I'm trying to solve a chance constrained programming (CCP) problem

$\min_x f_0(x, \xi), \text{ such that } \mathbb{P} ( f_i(x, \xi) \ge \alpha_i ) \le \epsilon_i, \text{ where } i = 1,2,\cdots, m$

Most of approaches to solve CCP problems are reformulating the chance constraint into some computationally tractable forms.

For example, the chance constraint $\mathbb{P}(\xi^\intercal x \ge b) \le \epsilon $ can be rewritten in 3 different ways (not equivalent)

assume $\xi$ satisfies a Gaussian distribution $\xi \sim N(\bar{\xi}, \Sigma)$, then $\mathbb{P}(\xi^\intercal x \ge b) \le \epsilon $ is

**equivalent**with $b - \bar{\xi}^\intercal x \ge \Phi^{-1}(1-\epsilon) || \Sigma^{1/2} x ||_2 $. This is a deterministic Second Order Cone Constraint. which is convex and will not cause intractable issues. (Please refer to Stephen Boyd's lecture notes for more details)Using the scenario approach in [1] Calafiore, Giuseppe C., and Marco C. Campi. "The scenario approach to robust control design." IEEE Transactions on Automatic Control 51.5 (2006): 742-753. Assume we have many samples $\xi^1, \xi^2,\cdots, \xi^N$ from unknown distribution of $\xi$. The chance constraint $\mathbb{P}(\xi^\intercal x \ge b) \le \epsilon $ is

**approximated**by

\begin{eqnarray} (\xi^1)^\intercal x \ge b\\ (\xi^2)^\intercal x \ge b\\ \vdots\\ (\xi^N)^\intercal x \ge b \end{eqnarray} which is a set of linear (deterministic) inequalities

- the convex approximation (Bernstein approximation) in [2] Nemirovski, Arkadi, and Alexander Shapiro. "Convex approximations of chance constrained programs." SIAM Journal on Optimization 17.4 (2006): 969-996. I will not write their solutions here since I don't want to scare you away.

All these approaches are reformulating the chance constraint into some computationally tractable forms (by which I mean current solvers like gruobi/cplex/mosek could handle).

**I'm wondering are there any scripts (preferably in Matlab or Python) that could convert a chance constraint into a deterministic form using the methods listed above?**

Or in the best case, **are there any solvers have incorporated the methods above and are able to solve chance constrained programming problems?**