A probabilistic analytic center cutting plane method for feasibility of uncertain LMIs
Automatica (Journal of IFAC)
An Integer Programming Approach for Linear Programs with Probabilistic Constraints
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
Mathematics of Operations Research
Cutting-set methods for robust convex optimization with pessimizing oracles
Optimization Methods & Software
Constructing Risk Measures from Uncertainty Sets
Operations Research
Constructing Uncertainty Sets for Robust Linear Optimization
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
A relaxation algorithm with a probabilistic guarantee for robust deviation optimization
Computational Optimization and Applications
Learning algorithms for link prediction based on chance constraints
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part I
Uncertainty and sensitivity analysis issues in support vector machines
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
Survey paper: Research on probabilistic methods for control system design
Automatica (Journal of IFAC)
SIAM Journal on Optimization
Theory and Applications of Robust Optimization
SIAM Review
A constraint sampling approach for multi-stage robust optimization
Automatica (Journal of IFAC)
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
Cutting plane algorithms for solving a stochastic edge-partition problem
Discrete Optimization
Direct data-driven portfolio optimization with guaranteed shortfall probability
Automatica (Journal of IFAC)
A Nonparametric Approach to Modeling Choice with Limited Data
Management Science
Control design for specifications on stochastic hybrid systems
Proceedings of the 16th international conference on Hybrid systems: computation and control
Convex Approximations of a Probabilistic Bicriteria Model with Disruptions
INFORMS Journal on Computing
Safe Approximations of Ambiguous Chance Constraints Using Historical Data
INFORMS Journal on Computing
Input design as a tool to improve the convergence of PEM
Automatica (Journal of IFAC)
Electronic Notes in Theoretical Computer Science (ENTCS)
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Many engineering problems can be cast as optimization problems subject to convex constraints that are parameterized by an uncertainty or ‘instance’ parameter. Two main approaches are generally available to tackle constrained optimization problems in presence of uncertainty: robust optimization and chance-constrained optimization. Robust optimization is a deterministic paradigm where one seeks a solution which simultaneously satisfies all possible constraint instances. In chance-constrained optimization a probability distribution is instead assumed on the uncertain parameters, and the constraints are enforced up to a pre-specified level of probability. Unfortunately however, both approaches lead to computationally intractable problem formulations.In this paper, we consider an alternative ‘randomized’ or ‘scenario’ approach for dealing with uncertainty in optimization, based on constraint sampling. In particular, we study the constrained optimization problem resulting by taking into account only a finite set of N constraints, chosen at random among the possible constraint instances of the uncertain problem. We show that the resulting randomized solution fails to satisfy only a small portion of the original constraints, provided that a sufficient number of samples is drawn. Our key result is to provide an efficient and explicit bound on the measure (probability or volume) of the original constraints that are possibly violated by the randomized solution. This volume rapidly decreases to zero as N is increased.