Robust Conic Convex Optimization and Its Applications
首发时间:2005-03-18
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.
keywords: Convex Conic Optimization Robust Optimization D-duality Convex
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Robust锥最优化及其应用
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。
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