Reduced Basis Techniques for Stochastic Problems

Stochastic Reduced Basis Methods

Multilevel and weighted reduced basis method for stochastic optimal control problems constrained by Stokes equations

In this paper we develop and analyze a multilevel weighted reduced basis method for solving stochastic optimal control problems constrained by Stokes equations. Existence and uniqueness of the stochastic optimal solution is proved by establishing the equivalence between the constrained optimization problem and a stochastic saddle point problem. Analytic regularity of the optimal solution in the...

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method [43, 1, 31, 30] has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method [28, 40, 33], primarily developed for solving parametric systems, has been recently used to deal with stochastic problems [7, 6]. In this work, we aim at comparing the performance of the two methods when applied t...

Weighted reduced basis method for stochastic optimal control problems with elliptic PDE constraint

In this paper we develop and analyze an efficient computational method for solving stochastic optimal control problems constrained by elliptic partial differential equation (PDE) with random input data. We first prove both existence and uniqueness of the optimal solution. Regularity of the optimal solution in the stochastic space is studied in view of the analysis of stochastic approximation er...

Approximation Techniques for Stochastic Combinatorial Optimization Problems

The focus of this thesis is on the design and analysis of algorithms for basic problems in Stochastic Optimization, speciVcally a class of fundamental combinatorial optimization problems where there is some form of uncertainty in the input. Since many interesting optimization problems are computationally intractable (NP-Hard), we resort to designing approximation algorithms which provably outpu...