Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
On Tractable Approximations of Uncertain Linear Matrix Inequalities Affected by Interval Uncertainty
SIAM Journal on Optimization
Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems
SIAM Journal on Optimization
Extended Matrix Cube Theorems with Applications to µ-Theory in Control
Mathematics of Operations Research
On Constraint Sampling in the Linear Programming Approach to Approximate Dynamic Programming
Mathematics of Operations Research
Uncertain convex programs: randomized solutions and confidence levels
Mathematical Programming: Series A and B
Ambiguous chance constrained problems and robust optimization
Mathematical Programming: Series A and B
Sums of random symmetric matrices and quadratic optimization under orthogonality constraints
Mathematical Programming: Series A and B
Convex Approximations of Chance Constrained Programs
SIAM Journal on Optimization
Quasi-convex designs of max-min linear BC precoding with outage QoS constraints
ISWCS'09 Proceedings of the 6th international conference on Symposium on Wireless Communication Systems
Safe Approximations of Ambiguous Chance Constraints Using Historical Data
INFORMS Journal on Computing
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In the paper we consider the chance-constrained version of an affinely perturbed linear matrix inequality (LMI) constraint, assuming the primitive perturbations to be independent with light-tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing a central role in chance-constrained linear/conic quadratic/semidefinite programming, are typically computationally intractable. The goal of this paper is to develop a tractable approximation to these chance constraints. Our approximation is based on measure concentration results and is given by an explicit system of LMIs. Thus, the approximation is computationally tractable; moreover, it is also safe, meaning that a feasible solution of the approximation is feasible for the chance constraint.