Pedro Borges

joint work with Mikhail Solodov, Claudia Sagastizábal

New Techniques for Sensitivity Analysis of Solution Mappings with Applications to Possibly Non-Convex Stochastic Programming

We introduce a well-behaved regularization of solution mappings of parametric convex problems that is single-valued and smooth. We do not assume strict complementarity or second order sufficiency. Such regularization gives a cheap upper smoothing for possibly non-convex optimal value functions. Classical first and second order derivatives of the regularized solution mappings can be obtained cheaply solving certain linear systems. For convex two-stage stochastic problems the interest of our techniques is assessed, comparing its numerical performance against a bundle method.

Shu Lu

Statistical inference for piecewise normal distributions and application to stochastic variational inequalities

Confidence intervals for the mean of a normal distribution with a known covariance matrix can be computed using closed-form formulas. In this talk, we consider a distribution that is the image of a normal distribution under a piecewise linear function, and provide a formula for computing confidence intervals for the mean of that distribution given a sample under certain conditions. We then apply this method to compute confidence intervals for the true solution of a stochastic variational inequality. This method is based on a closed-form formula which makes computation very efficient.