Proceedings of the 24th international conference on Machine learning
MIMO transceiver design via majorization theory
Foundations and Trends in Communications and Information Theory
Improved approximation bound for quadratic optimization problems with orthogonality constraints
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Interval Data Classification under Partial Information: A Chance-Constraint Approach
PAKDD '09 Proceedings of the 13th Pacific-Asia Conference on Advances in Knowledge Discovery and Data Mining
On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
Mathematics of Operations Research
Constructing Risk Measures from Uncertainty Sets
Operations Research
Constructing Uncertainty Sets for Robust Linear Optimization
Operations Research
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
Percentile Optimization for Markov Decision Processes with Parameter Uncertainty
Operations Research
Solving chance-constrained combinatorial problems to optimality
Computational Optimization and Applications
α-Conservative approximation for probabilistically constrained convex programs
Computational Optimization and Applications
Robust Approximation to Multiperiod Inventory Management
Operations Research
A Soft Robust Model for Optimization Under Ambiguity
Operations Research
Slow adaptive OFDMA systems through chance constrained programming
IEEE Transactions on Signal Processing
Scalable Heuristics for a Class of Chance-Constrained Stochastic Programs
INFORMS Journal on Computing
Approximation algorithms for reliable stochastic combinatorial optimization
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Neyman-Pearson Classification, Convexity and Stochastic Constraints
The Journal of Machine Learning Research
SIAM Journal on Optimization
Theory and Applications of Robust Optimization
SIAM Review
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
A robust approach to the chance-constrained knapsack problem
Operations Research Letters
Convexity and convex approximations of discrete-time stochastic control problems with constraints
Automatica (Journal of IFAC)
Stochastic Optimization of Sensor Placement for Diver Detection
Operations Research
Aspirational Preferences and Their Representation by Risk Measures
Management Science
Multiple Objectives Satisficing Under Uncertainty
Operations Research
Convex Approximations of a Probabilistic Bicriteria Model with Disruptions
INFORMS Journal on Computing
Reliable approximations of probability-constrained stochastic linear-quadratic control
Automatica (Journal of IFAC)
Probabilistic planning for continuous dynamic systems under bounded risk
Journal of Artificial Intelligence Research
Safe Approximations of Ambiguous Chance Constraints Using Historical Data
INFORMS Journal on Computing
Stochastic Operating Room Scheduling for High-Volume Specialties Under Block Booking
INFORMS Journal on Computing
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We consider a chance constrained problem, where one seeks to minimize a convex objective over solutions satisfying, with a given close to one probability, a system of randomly perturbed convex constraints. This problem may happen to be computationally intractable; our goal is to build its computationally tractable approximation, i.e., an efficiently solvable deterministic optimization program with the feasible set contained in the chance constrained problem. We construct a general class of such convex conservative approximations of the corresponding chance constrained problem. Moreover, under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent-of-each-other random variables, we build a large deviation-type approximation, referred to as “Bernstein approximation,” of the chance constrained problem. This approximation is convex and efficiently solvable. We propose a simulation-based scheme for bounding the optimal value in the chance constrained problem and report numerical experiments aimed at comparing the Bernstein and well-known scenario approximation approaches. Finally, we extend our construction to the case of ambiguous chance constrained problems, where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly, while the chance constraint should be satisfied for every distribution given by this set.