Robust锥最优化及其应用
Robust Conic Convex Optimization and Its Applications
摘要
由于内点法的出现，锥最优化逐渐成为而且已经成为一个活跃的研究领域。但在实际生活中，由于不确定性的存在，我们尤其关注最优化问题的最优解的robust性。本文把不确定性考虑进凸锥最优化问题，在D-对偶理论的框架内把原问题的确定性等价问题表示出来了。对于这样的问题，我们只要计算一个D-对偶锥就可以了。但一般来说D-对偶锥是很难计算的。本文对某些特殊情形导出了其D-对偶锥。我们把我们的理论应用于robust定位、robust拟合、robust多阶段投资并导出了其确定性等价问题。
Abstract
Research of convex conic optimization becomes spry thanks to the powerful interior point method while due to uncertainty in practice, robustness of a solution of an optimization problem is emphasized. This article incorporates robustness into a general
convex conic optimization problem and shows its deterministic equivalence under the D-duality framework, in which one needs only to compute a D-induced convex cone, which is generally difficult. While for some special case this paper shows that its tractable. Three kinds of
applications in robust location, robust fitting and robust
multi-stage investment problems are shown to illustrate the
unification of this framework.关键词
凸锥最优化/robust最优化/D-对偶/凸锥/定位/拟合/多阶段投资Key words
Convex Conic Optimization/Robust Optimization/D-duality/Convex引用本文复制引用
孙楚仁.Robust锥最优化及其应用[EB/OL].(2005-03-18)[2026-04-02].http://www.paper.edu.cn/releasepaper/content/200503-115.学科分类
数学
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