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# Exact penalization, level function method and modified cutting-plane method for stochastic programs with second order stochastic dominance constraints

Sun, Hailin, Xu, Huifu, Meskarian, Rudabeh and Wang, Yong (2013) Exact penalization, level function method and modified cutting-plane method for stochastic programs with second order stochastic dominance constraints. SIAM Journal on Optimization, 23 (1), 602-631.

Record type: Article

## Abstract

Level function methods and cutting-plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance (SSD) constraints. A level function method requires an exact penalization setup because it can only be applied to the objective function, not the constraints. Slater constraint qualification (SCQ) is often needed for deriving exact penalization. It is well known that SSD usually does not satisfy SCQ and various relaxation schemes have been proposed so that the relaxed problem satisfies the SCQ. In this paper, we show that under some moderate conditions the desired constraint qualification can be guaranteed through some appropriate reformulation of the constraints rather than relaxation. Exact penalization schemes based on $L_1$-norm and $L_\infty$-norm are subsequently derived through Robinson's error bound on convex systems and Clarke's exact penalty function theorem. Moreover, we propose a modified cutting-plane method which constructs a cutting-plane through the maximum of the reformulated constraint functions. In comparison with the existing cutting-plane methods, it is numerically more efficient because only a single cutting plane is constructed and added at each iteration. We have carried out a number of numerical experiments and the results show that our methods display better performances particularly in the case when the underlying functions are nonlinear w.r.t. decision variables.

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Published date: 2013
Organisations: Operational Research

## Identifiers

Local EPrints ID: 390730
URI: http://eprints.soton.ac.uk/id/eprint/390730
ISSN: 1052-6234
PURE UUID: d3b255cc-69ee-4a43-a308-cf4f0a10f7cd
ORCID for Huifu Xu: orcid.org/0000-0001-8307-2920

## Catalogue record

Date deposited: 06 Apr 2016 14:43

## Contributors

Author: Hailin Sun
Author: Huifu Xu
Author: Rudabeh Meskarian
Author: Yong Wang