We provide an explicit gradient formula for linear chance constraints under a (possibly singular) multivariate Gaussian distribution. This formula allows one to reduce the calculus of gradients to the calculus of values of the same type of chance constraints (in smaller dimension and with different distribution parameters). This is an important aspect for the numerical solution of stochastic op...

We introduce two methods for approximation to distribution of weighted sum of chi-square random variables. These methods can be more useful than the known methods in literature to transform chi-square type chance constrained programming (CCP) problem into deterministic problem. Therefore, these are compared with Sengupta (1970)’s method. Some examples are illustrated for the purpose of comparin...

A distributionally robust joint chance constraint involves a set of uncertain linear inequalities which can be violated up to a given probability threshold , over a given family of probability distributions of the uncertain parameters. A conservative approximation of a joint chance constraint, often referred to as a Bonferroni approximation, uses the union bound to approximate the joint chance ...

We present a new method for solving stochastic programs with joint chance constraints with discretely distributed random data. The problem can be reformulated as a large-scale mixed 0-1 integer program. We derive a new class of optimality cuts based on irreducibly infeasible subsets (IIS) of an LP defined by requiring that all scenarios be satisfied and propose a method for improving the upper ...

We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6, 11]. The obtained problems with penalties and with a fixed set of feasible so...

Physically grounded AI systems consisting of multiple mobile agents need to conduct complicated tasks cooperatively in dynamic, uncertain environment. Two important capabilities for such systems are robust kinodynamic path planning and distributed plan execution on a hybrid discrete/continuous plant. For example, a fleet of autonomous underwater vehicles (AUV) shown in Figure 1, which conducts ...

This paper investigates the computational aspects of distributionally robust chance constrained optimization problems. In contrast to previous research that mainly focused on the linear case (with a few exceptions discussed in detail below), we consider the case where the constraints can be non-linear to the decision variable, and in particular to the uncertain parameters. This formulation is o...

Natural and man-created disasters, such as hurricanes, earthquakes, tsunamis, accidents and terrorist attacks, have shown the need for quick evacuation. Evacuation routes are mostly based on the capacities of the road network. However, in extreme cases such as earthquakes, road network infrastructure may adversely be affected, and may not supply the required capacities. If for various situation...

We investigate the convexity of chance constraints with independent random variables. It will be shown, how concavity properties of the mapping related to the decision vector have to be combined with a suitable property of decrease for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels. It turns out that the required decrease can be ve...