Chance--constrained Optimization with Stochastically Dependent Perturbations.
详细信息
- 作者：Wang ; Kuncheng.
- 学历：Doctor
- 年：2012
- 关键词：chance--constrained programming ; dependence perturb
- 毕业院校：The Chinese University of Hong Kong
- Department：Systems Engineering and Engineering Management.
- ISBN：9781267985927
- CBH：3537665
- Country：China
- 语种：English
- FileSize：618508
- Pages：115
文摘
The wide applicability of chance--constrained programming,together with advances in convex optimization and probability theory,has created a surge of interest in finding efficient methods for processing chance constraints in recent years. One of the successes is the development of so--called safe tractable approximations of chance--constrained programs,where a chance constraint is replaced by a deterministic and efficiently computable inner approximation. Currently,such an approach applies mainly to chance--constrained linear inequalities,in which the data perturbations are either independent or define a known covariance matrix. However,its applicability to the case of chance--constrained conic inequalities with dependent perturbations---which arises in supply chain management,finance,control and signal processing applications---remains largely unexplored. In this thesis,we consider the problem of processing chance--constrained affinely perturbed linear matrix inequalities,in which the perturbations are not necessarily independent,and the only information available about the dependence structure is a list of independence relations. Using large deviation bounds for matrix--valued random variables,we develop safe tractable approximations of those chance constraints. Extensions to the Matrix CVaR Conditional Value--at--Risk) risk measure and general polynomials perturbations are also provided separately. Further more,we show that the chance--constrained linear matrix inequalities optimization problem can be converted to a robust optimization problem by constructing the uncertainty set of the corresponding robust counterpart. A nice feature of our approximations is that they can be expressed as systems of linear matrix inequalities,thus allowing them to be solved easily and efficiently by off--the--shelf optimization solvers. We also provide a numerical illustration of our constructions through a problem in control theory and a portfolio VaR Value-at-Risk) optimization problem.