Linear Matrix Inequalities with Stochastically Dependent Perturbations and Applications to Chance-Constrained Semidefinite Optimization

Abstract

The wide applicability of chance-constrained programming, together with advances in convex optimization and probability theory, has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so-called safe tractable approximations of chance-constrained programs, where a chance constraint is replaced by a deterministic and efficiently computable inner approximation. Currently, such an approach applies mainly to chance-constrained linear inequalities, in which the data perturbations either are independent or define a known covariance matrix. However, its applicability to chance-constrained conic inequalities with dependent perturbations---which arises in finance, control, and signal processing applications---remains largely unexplored. In this paper, we develop safe tractable approximations of chance-constrained affinely perturbed linear matrix inequalities, in which the perturbations are not necessarily independent,...