A class of volumetric barrier decomposition algorithms for stochastic quadratic programming

Ariyawansa, K. A.; Zhu, Yuntao

doi:10.1016/j.amc.2006.08.171

Cited by 9 publications

(20 citation statements)

References 8 publications

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“…The specialization is a new class of algorithms for SLPs. Indeed, in [6] we show that we can go further by showing how appropriate modification of the techniques utilized in the present paper leads to a class of new volumetric barrier decomposition algorithms for stochastic quadratic programs with quadratic recourse.…”

Section: Discussionmentioning

confidence: 79%

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

Ariyawansa

Zhu

2010

Math. Comp.

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Abstract. Ariyawansa and Zhu have recently proposed a new class of optimization problems termed stochastic semidefinite programs (SSDPs). SSDPs may be viewed as an extension of two-stage stochastic (linear) programs with recourse (SLPs). Zhao has derived a decomposition algorithm for SLPs based on a logarithmic barrier and proved its polynomial complexity. Mehrotra and Ozevin have extended the work of Zhao to the case of SSDPs to derive a polynomial logarithmic barrier decomposition algorithm for SSDPs. An alternative to the logarithmic barrier is the volumetric barrier of Vaidya. There is no work based on the volumetric barrier analogous to that of Zhao for SLPs or to the work of Mehrotra andÖzevin for SSDPs. The purpose of this paper is to derive a class of volumetric barrier decomposition algorithms for SSDPs, and to prove polynomial complexity of certain members of the class.

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Section: Discussionmentioning

confidence: 79%

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

Ariyawansa

Zhu

2010

Math. Comp.

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“…As a result, it is now straightforward to develop primal path following interior point algorithms for solving SQSOCP ( [5,6]). In this section, we introduce the volumetric barrier decomposition-based interior point algorithm for solving this problem.…”

Section: The Two-stage Sqsocp Volumetric Barrier Decomposition Algorithmmentioning

confidence: 99%

Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming

Alzalg

2015

Applied Mathematics and Computation

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“…Note that, for a given l, the optimality conditions for the first-stage problem (11) are r x e gðl; xÞ À A T k ¼ 0;…”

Section: Problem Formulation and Assumptionsmentioning

confidence: 99%

“…Throughout the paper, for a given l > 0, we denote the optimal solution of the first-stage problem (11) by xðlÞ (or simply by x), and the solutions of the optimality conditions (10) by (ỹ ðkÞ ðl; xÞ; z ðkÞ ðl; xÞ; e s ðkÞ ðl; xÞ) (or simply by (ỹ ðkÞ ; z ðkÞ ; e s ðkÞ )). The SQSOCP (11) and (12) can be equivalently written as a deterministic quadratic second-order cone programming: max e gðl; xÞ :…”

Section: Problem Formulation and Assumptionsmentioning

confidence: 99%

Decomposition-based interior point methods for stochastic quadratic second-order cone programming

Alzalg

2014

Applied Mathematics and Computation

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A class of volumetric barrier decomposition algorithms for stochastic quadratic programming

Cited by 9 publications

References 8 publications

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

A class of polynomial volumetric barrier decomposition algorithms for stochastic semidefinite programming

Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming

Decomposition-based interior point methods for stochastic quadratic second-order cone programming

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