Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038     

Computational experience with a bundle approach for semidefinite cutting plane relaxations of Max-Cut and Equipartition

We propose a dynamic version of the bundle method to get approximate solutions to semidefinite programs with a nearly arbitrary number of linear inequalities. Our approach is based on Lagrangian duality, where the inequalities are dualized, and only a basic set of constraints is maintained explicitly. This leads to function evaluations requiring to solve a relatively simple semidefinite program. Our approach provides accurate solutions to semidefinite relaxations of the Max-Cut and the Equipartition problem, which are not achievable by direct approaches based only on interior-point methods. Received: April, 2004 The last author gratefully acknowledges the support from the Austrian Science Foundation FWF Project P12660-MAT.     

Symmetrized-lexicographic order and the method of points

A variant of lexicographic order called symmetrized-lexicographic order is defined. The symmetrized-lexicographic order finds its application in the goal programming procedure called the method of points. The symmetrized-lexicographic order is shown to be representable using linear algebra and, thus, the method of points can be implemented as a linear programming problem.     

On constructing expert Betas for single-index model

The aim of this paper is to design flexible decision making models for portfolio selection including expert’s knowledge and imprecise preferences provided by financial analysts and investors, respectively.     

Multistage stochastic convex programs: Duality and its implications

In this paper, we study alternative primal and dual formulations of multistage stochastic convex programs (SP). The alternative dual problems which can be traced to the alternative primal representations, lead to stochastic analogs of standard deterministic constructs such as conjugate functions and Lagrangians. One of the by-products of this approach is that the development does not depend on dynamic programming (DP) type recursive arguments, and is therefore applicable to problems in which the objective function is non-separable (in the DP sense). Moreover, the treatment allows us to handle both continuous and discrete random variables with equal ease. We also investigate properties of the expected value of perfect information (EVPI) within the context of SP, and the connection between EVPI and nonanticipativity of optimal multipliers. Our study reveals that there exist optimal multipliers that are nonanticipative if, and only if, the EVPI is zero. Finally, we provide interpretations of the retroactive nature of the dual multipliers. This work was supported by NSF grant DMII-9414680.     

具有独立子块的大系统目标规划问题的解法

分解之后如何进行协调解决大系统规划问题的关键．本文通过利用子系统目标值所提供的信息进行大系统分解之后的协调，并提出了求解具有独立子块的大系统规划问题的串式调优法，同时研究了有关原问题和各子问题最优解的性质．     

The Hierarchical compromise programming

This paper presents a multicriteria decision making method, the Hierarchical Compromise Programming (HCP), which combines a hierarchical structure for the modelization of a problem with the minimization of the distance to an ideal point as a resolution procedure. The proposed method allows the application of a model based on the minimization of a distance function, with tangible and intangible aspects. This research has been partially supported by the project SISDEMA: UN SISTEMA DECISIONAL AMBIENTAL (ref.: PMA-2196 CONSID-DGA)     

Worst-case distribution analysis of stochastic programs

We show that for even quasi-concave objective functions the worst-case distribution, with respect to a family of unimodal distributions, of a stochastic programming problem is a uniform distribution. This extends the so-called ``Uniformity Principle' of Barmish and Lagoa (1997) where the objective function is the indicator function of a convex symmetric set.     

了本岛津产ICPl000型等离子体发射光谱仪的改造方法（软件部分）

提出了日本岛津1000型ICP改造后的软件设计方法，详细介绍了核心控制程序软件、服务程序框图和终端操作界面，阐明了标定放大系数、制作校准曲线的原理和方法。为该种大型精密光学仪器的改造做了有益的尝试。     

解线性规划问题的梯度投影法

本文叙述了一个求解线性规划问题的梯度投影法,导出了投影矩阵的递推公式,利用此公式可大大减少每次迭代所需的计算量。实例计算表明,本文给出的算法是一有效的算法,在某些方面它要优于Karmarkar算法和单纯形法。