Global Search for Bilevel Optimization with Quadratic Data

Strekalovsky, Alexander S.; Орлов, А. В.

doi:10.1007/978-3-030-52119-6_11

Cited by 6 publications

(3 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In particular, it allows one to reformulate two-stage stochastic programming problems, whose second stage problem has DC (Difference-of-Convex) objective function and DC constraints, as equivalent unconstrained DC optimization problems and apply the well-developed apparatus of DC optimization to find their solutions (cf. analogous results for bilevel programming problems in [33,42]). Let us also note that exact penalty functions for singlestage stochastic programming were analysed in [24].…”

Section: Introductionmentioning

confidence: 72%

See 1 more Smart Citation

Codifferentials and Quasidifferentials of the Expectation of Nonsmooth Random Integrands and Two-Stage Stochastic Programming

Долгополик¹

2021

Preprint

View full text Add to dashboard Cite

This work is devoted to an analysis of exact penalty functions and optimality conditions for nonsmooth two-stage stochastic programming problems. To this end, we first study the co-/quasi-differentiability of the expectation of nonsmooth random integrands and obtain explicit formulae for its co-and quasidifferential under some natural assumptions on the integrand. Then we analyse exact penalty functions for a variational reformulation of two-stage stochastic programming problems and obtain sufficient conditions for the global exactness of these functions with two different penalty terms. In the end of the paper, we combine our results on the co-/quasi-differentiability of the expectation of nonsmooth random integrands and exact penalty functions to derive optimality conditions for nonsmooth two-stage stochastic programming problems in terms of codifferentials.

show abstract

Section: Introductionmentioning

confidence: 72%

“…Thus, Theorem 3 opens a way for applications of DC programming algorithms to two-stage stochastic programming problems (cf. [33,42]).…”

Section: Exact Penalty Functionsmentioning

confidence: 99%