English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We consider risk-averse convex stochastic programs expressed in terms ofextended polyhedral risk measures. We derive computable confidence intervals onthe optimal value of such stochastic programs using the Robust StochasticApproximation and the Stochastic Mirror Descent (SMD) algorithms. When theobjective functions are uniformly convex, we also propose a multistep extensionof the Stochastic Mirror Descent algorithm and obtain confidence intervals onboth the optimal values and optimal solutions. Numerical simulations show thatour confidence intervals are much less conservative and are quicker to computethan previously obtained confidence intervals for SMD and that the multistepStochastic Mirror Descent algorithm can obtain a good approximate solution muchquicker than its nonmultistep counterpart. Our confidence intervals are alsomore reliable than asymptotic confidence intervals when the sample size is notmuch larger than the problem size.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures