In this paper, we consider the static output feedback （SOF） H∞-synthesis problem posed as a nonlinear semi-definite programming （NSDP） problem. Two numerical algorithms are developed to tackle the NSDP problem by...
详细信息
In this paper, we consider the static output feedback （SOF） H∞-synthesis problem posed as a nonlinear semi-definite programming （NSDP） problem. Two numerical algorithms are developed to tackle the NSDP problem by solving the corresponding Karush- Kuhn-Tucker first-order necessary optimality conditions iteratively. Numerical results for various benchmark problems illustrating the performance of the proposed methods are given.
To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR appro...
详细信息
To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR approach and formulate the corresponding problems as semi-definite programs. Moreover, we present some numerical results with real market data. (C) 2006 Elsevier B.V. All rights reserved.
The present methods for obtaining the optimal Lewenestein-Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein-Sanpera decom...
详细信息
The present methods for obtaining the optimal Lewenestein-Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein-Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein-Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2 circle times 3 Bell decomposable state, the d circle times d Werner and isotropic states, a one parameter 3 circle times 3 state, and finally a multi-partite isotropic state.
Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have...
详细信息
ISBN:
(纸本)9781424414970
Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have recently introduced a stochastic global optimization method, called semi-definite programming based Underestimation (SDU) [1], that constructs a convex quadratic under-estimator to the free energy funnel based on a sample of energy function evaluations and uses the quadratic under-estimator to guide future sampling. In this paper we show that the parameterization of SE(3) has a significant impact on the effectiveness of SDU and introduce a parameterization that dramatically reduces the number of very costly energy function evaluations. The resulting algorithm represents a significant gain (more than an order of magnitude) in computational efficiency compared to state-of-the-art Monte Carlo-based algorithms used for the same purpose.
The need to track a subspace describing well a stream of points arises in many signal processing applications. In this work, we present a very efficient algorithm using a machine learning approach, which its goal is t...
详细信息
ISBN:
(纸本)9781605603162
The need to track a subspace describing well a stream of points arises in many signal processing applications. In this work, we present a very efficient algorithm using a machine learning approach, which its goal is to de-noise the stream of input points. The algorithm guarantees the orthonormality of the representation it uses. We demonstrate the merits of our approach using simulations.
Ensemble methods provide a principled framework in which to build high performance classifiers and represent many types of data. As a result, these methods can be useful for making inferences about biometric and biolo...
详细信息
ISBN:
(纸本)9780819466884
Ensemble methods provide a principled framework in which to build high performance classifiers and represent many types of data. As a result, these methods can be useful for making inferences about biometric and biological events. We introduce a novel ensemble method for combining multiple representations (or views). The method is a multiple view generalization of AdaBoost. Similar to AdaBoost, base classifiers are independently built from each represetation. Unlike AdaBoost, however, all data types share the same sampling distribution computed from the base classifier having the smallest error rate among input sources. As a result, the most consistent data type dominates over time, thereby significantly reducing sensitivity to noise. The method is applied to the problem of facial and gender prediction based on biometric traits. The new method outperforms several competing techniques including kernel-based data fusion, and is provably better than AdaBoost trained on any single type of data.
Support Vector Machines have been a dominant learning technique for almost ten years, moreover they have been applied to supervised learning problems. Recently two-class unsupervised and semi-supervised classification...
详细信息
ISBN:
(纸本)9783540725879
Support Vector Machines have been a dominant learning technique for almost ten years, moreover they have been applied to supervised learning problems. Recently two-class unsupervised and semi-supervised classification problems based on Bounded C-Support Vector Machines and Bounded v-Support Vector Machines are relaxed to semi-definite programming[4][11]. In this paper we will present another version to unsupervised and semi-supervised classification problems based on Lagrangian Support Vector Machines, which trained by convex relaxation of the training criterion: find a labelling that yield a maximum margin on the training data. But the problems have difficulty to compute, we will find their semi-definite relaxations that can approximate them well. Experimental results show that our new unsupervised and semi-supervised classification algorithms often obtain almost the same accurate results as the unsupervised and semi-supervised methods [4][11], while considerably faster than them.
Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have...
详细信息
ISBN:
(纸本)9781424414970;1424414970
Formulated as an optimization problem, the final stages of protein docking can be viewed as optimizing a very noisy funnel-like function on the space of rigid body motions, the (special) Euclidean group SE(3). We have recently introduced a stochastic global optimization method, called semi-definite programming based Underestimation (SDU) [1], that constructs a convex quadratic under-estimator to the free energy funnel based on a sample of energy function evaluations and uses the quadratic under-estimator to guide future sampling. In this paper we show that the parameterization of SE(3) has a significant impact on the effectiveness of SDU and introduce a parameterization that dramatically reduces the number of very costly energy function evaluations. The resulting algorithm represents a significant gain (more than an order of magnitude) in computational efficiency compared to state-of-the-art Monte Carlo-based algorithms used for the same purpose.
We will propose an outer-approximation (cutting plane) method for minimizing a function f(X) subject to semi-definite constraints on the variables X is an element of R-nxn. A number of efficient algorithms have been p...
详细信息
We will propose an outer-approximation (cutting plane) method for minimizing a function f(X) subject to semi-definite constraints on the variables X is an element of R-nxn. A number of efficient algorithms have been proposed when the objective function is linear. However, there are very few practical algorithms when the objective function is nonlinear. An algorithm to be proposed here is a kind of outer-approximation( cutting plane) method, which has been successfully applied to several low rank global optimization problems including generalized convex multiplicative programming problems and generalized linear fractional programming problems, etc. We will show that this algorithm works well when f is convex and n is relatively small. Also, we will provide the proof of its convergence under various technical assumptions.
暂无评论