Linear matrix inequalities (LMI) are used to solve robust portfolio problems and many other control problems. ellipsoid algorithm and interior-point method are used to solve EAU. In this paper, we consider a robust po...
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ISBN:
(纸本)9789881563958
Linear matrix inequalities (LMI) are used to solve robust portfolio problems and many other control problems. ellipsoid algorithm and interior-point method are used to solve EAU. In this paper, we consider a robust portfolio model based on Markowitz theory that minimizes the risk at a certain level of return. We turn the model into the LMI with constraints and use ellipsoid algorithm and interior-point method to solve it. A numerical simulation in stock portfolio is given to prove the validity of the method. Because the rate of return is change over time, in order to make the result robust, we use exponentially weighted moving-average (EWMA) method to compute the covariance matrices. Due to the highly reliable result, the model can provide a reference for investors to make decision on portfolio.
A recent seminal result of Racke is that for any network there is an oblivious routing algorithm with a polylog competitive ratio with respect to congestion. Unfortunately, Racke's construction is not polynomial t...
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ISBN:
(纸本)9781581136746
A recent seminal result of Racke is that for any network there is an oblivious routing algorithm with a polylog competitive ratio with respect to congestion. Unfortunately, Racke's construction is not polynomial time. We give a polynomial time construction that guarantee's Racke's bounds, and more generally gives the true optimal ratio for any network.
It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly combinatorial) fea...
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ISBN:
(纸本)9781611972511
It was recently shown in [12] that revenue optimization can be computationally efficiently reduced to welfare optimization in all multi-dimensional Bayesian auction problems with arbitrary (possibly combinatorial) feasibility constraints and independent additive bidders with arbitrary (possibly combinatorial) demand constraints. This reduction provides a poly-time solution to the optimal mechanism design problem in all auction settings where welfare optimization can be solved efficiently, but it is fragile to approximation and cannot provide solutions to settings where welfare maximization can only be tractably approximated. In this paper, we extend the reduction to accommodate approximation algorithms, providing an approximation preserving reduction from (truthful) revenue maximization to (not necessarily truthful) welfare maximization. The mechanisms output by our reduction choose allocations via blackbox calls to welfare approximation on randomly selected inputs, thereby generalizing also our earlier structural results on optimal multi-dimensional mechanisms to approximately optimal mechanisms. Unlike [12], our results here are obtained through novel uses of the ellipsoid algorithm and other optimization techniques over non-convex regions.
Linear matrix inequalities（LMI） are used to solve robust portfolio problems and many other control problems. ellipsoid algorithm and interior-point method are used to solve LMI. In this paper, we consider a robust p...
详细信息
Linear matrix inequalities（LMI） are used to solve robust portfolio problems and many other control problems. ellipsoid algorithm and interior-point method are used to solve LMI. In this paper, we consider a robust portfolio model based on Markowitz theory that minimizes the risk at a certain level of return. We turn the model into the LMI with constraints and use ellipsoid algorithm and interior-point method to solve it. A numerical simulation in stock portfolio is given to prove the validity of the method. Because the rate of return is change over time, in order to make the result robust, we use exponentially weighted moving-average（EWMA） method to compute the covariance matrices. Due to the highly reliable result, the model can provide a reference for investors to make decision on portfolio.
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