Document Zbl 1484.90055

Geiersbach, Caroline; Wollner, Winnifried

Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraints. (English) Zbl 1484.90055

SIAM J. Optim. 31, No. 4, 2455-2480 (2021).

Stochastic optimization problems in abstract spaces are considered related to two-stage stochastic programs (stochastic programs with recourse): Minimize a convex expectation-valued function \(J=J(x_1,x_2(\cdot))\) subject to a convex constraint for a deterministic variable \(x_1\) and an almost sure (a.s.) convex constraint, such as an a.s. bound depending on the deterministic variable \(x_1\), for a second, stochastic variable \(x_2 = x_2(\omega)\). The aim of the article is to provide necessary and sufficient optimality conditions for this problem. Using the perturbation approach, the existence of saddle points of a certain generalized Lagrangian is shown, and Karush-Kuhn-Tucker (KKT) optimality conditions are derived. A model problem is presented, and a concrete example is given.

Reviewer: Kurt Marti (München)

Cited in 4 Documents

MSC:

90C15	Stochastic programming
49K99	Optimality conditions
49N15	Duality theory (optimization)

Keywords:

stochastic optimization problems in abstract spaces; convex stochastic optimization; optimality conditions; two-stage stochastic optimization; regular Lagrange multipliers; duality

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Full Text: DOI arXiv

References:

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