A Confidence Region Approach to Tuning for Variable Selection

We develop an approach to tuning of penalized regression variable selection methods by calculating the sparsest estimator contained in a confidence region of a specified level. Because confidence intervals/regions are generally understood, tuning penalized regression methods in this way is intuitive and more easily understood by scientists and practitioners. More importantly, our work shows that tuning to a fixed confidence level often performs better than tuning via the common methods based on Akaike information criterion (AIC), Bayesian information criterion (BIC), or cross-validation (CV) over a wide range of sample sizes and levels of sparsity. Additionally, we prove that by tuning with a sequence of confidence levels converging to one, asymptotic selection consistency is obtained, and with a simple two-stage procedure, an oracle property is achieved. The confidence-region-based tuning parameter is easily calculated using output from existing penalized regression computer packages. Our work also shows how to map any penalty parameter to a corresponding confidence coefficient. This mapping facilitates comparisons of tuning parameter selection methods such as AIC, BIC, and CV, and reveals that the resulting tuning parameters correspond to confidence levels that are extremely low, and can vary greatly across datasets. Supplemental materials for the article are available online.     

二元样条的并行算法（英）

In this paper, we propose an algorithm for the reduction of a real sparse matrix that arises from the construction of certain spline surfaces to ‘block diagonal’ form. The approach is to aggregate matrix elements in similar position and to apply them in a blocked fashion, thus splitting the initial linear system into independent and parallelizable linear subsystems. The results suggest that it is possible to use a large number of processors to solve the above matrix problem at a relatively fine granularity.     

Optimal Control Approach to Nonlinear Diffusion Equations Driven by Wiener Noise

The stochastic nonlinear infinite-dimensional equations of gradient type and with additive Wiener noise can be reduced to an optimal convex control problem via Brezis–Ekeland duality device. This approach is illustrated here on a few classes of nonlinear stochastic parabolic equations which are relevant as diffusion models under stochastic Gaussian perturbations, and image restoring technique.     

A Group-Theoretic Approach to Parameter Identifiability of PDE Systems

The contribution is devoted to the parameter identifiability problem of (nonlinear) PDE systems. Especially, we discuss the (local) identifiability of parameters along a trajectory. The analysis relies on a coordinate-free formulation for systems, including boundary conditions, and we motivate an approach by (Lie) transformation groups, whose success for PDE systems depends on a consequent extent to the accompanying boundary conditions. The (non-)identifiability of parameters is related to the (non-)existence of group generators, wherewith (local) conditions can be derived. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

广义系统动态输出反馈控制设计的新方法

对于连续时间的广义系统,基于线性矩阵不等式(LMI),提出了动态输出反馈H_∞控制设计的新方法.给出了广义系统动态输出反馈H_∞控制存在的充分条件.通过求解线性矩阵不等式和矩阵方程实现控制的设计.所提出确定控制的方法是简洁和易于实现的.一个数值例子说明了提出方法的设计过程和控制的有效性.     

A Quality Control Approach for Monitoring Inventory Stock Levels

In this paper we develop a new approach to monitor the accuracy of an inventory management system. A recorded stock level is considered accurate when the recorded level agrees with the actual stock level, otherwise there is an error. In practice, management relies on methods to measure or assure inventory accuracy not necessarily developed for this purpose. Our methodology is based on the average absolute relative difference as a simple analytical measure for inventory accuracy (AC _N ). The approach captures the status of accuracy in an inventory and allows for greater understanding of what affects inaccuracy since the theoretical measure of accuracy is composed of several parameters representing the incidence and proportion of both overstock and understock. The implementation of the methodology is constrained because complete inspection of the inventory is very expensive in most situations, so we develop the sample analogue of the accuracy measure (AC _n ) and discuss sampling strategies. The accuracy of the inventory system is monitored by incorporating AC _n into a univariate control chart.     

A Wave-Based Approach to Adaptively Control Self-Excited Vibrations in Drill-Strings

Due to their small diameter-to-length-ratio, drill-strings are vulnerable to torsional vibrations. Moreover, the string is exposed to unknown or uncertain time-variant and nonlinear loads (e.g. friction with falling friction characteristics, contact with the borehole, differential sticking), which can result in severe torsional vibrations and stick-slip. The control law for the boundary controller at the top drive of the string needs to adapt to those unknown loads in order to stabilize the vibrations. The torsional vibrations of a drill-string are governed by the wave equation. Analytical solutions and control laws are often based on a separation of the dynamics into a time- and a space-dependent part (modal representation). Here, we decompose the vibrations into two traveling waves according to the D'Alembert solution, using only few measurements along the string. The wave which travels up the string is then compensated by the actuator at the top drive. With this compensation, the upward-traveling wave is no longer reflected back into the string and vibration energy is absorbed, thus stabilizing the torsional vibrations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于Hill方程稳定性准则的控制方法证明

Optimal estimates of the stability of Hill‘s equation are obtained. The discussion is based on Pontryagin‘s maximum principle.     

求解无限维线性二次最优控制问题的一种新的途径

本文借助Ｃ_０半群的Ｙｏｓｉｄａ近似构造无限维线性二次最优控制问题的相应近似，证明了后者的最优控制、Ｒｉｃｃａｔｉ方程之解（从而反馈算子）和最优状态函数均一致强收敛，极限即为原问题的解．     

A Variational Approach to Perturbation Feedback Control for Optimal Control Problems with Terminal Constraints and Free Terminal Time

Set-Valued and Variational Analysis - Using the method of characteristics, for an optimal control problem with terminal constraints and free terminal time, we construct a family of extremals along...     

A Dynamic Programming Approach for Approximate Optimal Control for Cancer Therapy

In the last 15 years, tumor anti-angiogenesis became an active area of research in medicine and also in mathematical biology, and several models of dynamics and optimal controls of angiogenesis have been described. We use the Hamilton–Jacobi approach to study the numerical analysis of approximate optimal solutions to some of those models earlier analysed from the point of necessary optimality conditions in the series of papers by Ledzewicz and Schaettler.     

A New Two-Model Approach for Optimizing Control of Large-Scale Steady-State Systems

A novel two-model approach for hierarchical system optimizationand parameter estimation of large-scale industrial processesis described which is considerably more efficient and reliablethan previous hierarchical methods for integrated system optimizationand parameter estimation (ISOPE), in the sense that it takesfar fewer changes of controller set points to produce the realoptimum, and its convergent conditions are weaker. Other advantages of this new approach are that the number ofcontroller set-point changes does not depend on the number ofinequality constraints that are tight at the optimum, and itis possible to provide sufficient conditions for global convergencewhich are nearly the same as those of the centralized ISOPEmethod. Optimality of the algorithm is examined, and a proof of theglobal convergence of the algorithm is presented. Computer simulationsare used to demonstrate the behaviour of the algorithm.     

A New Approach to Linearly Perturbed Riccati Equations Arising in Stochastic Control

In this paper a linearly perturbed version of the well-known matrix Riccati equations which arise in certain stochastic optimal control problems is studied. Via the concepts of mean square stabilizability and mean square detectability we improve previous results on both the convergence properties of the linearly perturbed Riccati differential equation and the solutions of the linearly perturbed algebraic Riccati equation. Furthermore, our approach unifies, in some way, the study for this class of Riccati equations with the one for classical theory, by eliminating a certain inconvenient assumption used in previous works (e.g., [10] and [26]). The results are derived under relatively weaker assumptions and include, inter alia, the following: (a) An extension of Theorem 4.1 of [26] to handle systems not necessarily observable. (b) The existence of a strong solution, subject only to the mean square stabilizability assumption. (c) Conditions for the existence and uniqueness of stabilizing solutions for systems not necessarily detectable. (d) Conditions for the existence and uniqueness of mean square stabilizing solutions instead of just stabilizing. (e) Relaxing the assumptions for convergence of the solution of the linearly perturbed Riccati differential equation and deriving new convergence results for systems not necessarily observable. Accepted 30 July 1996     

A Penalty Approach to Optimal Control of Allen-Cahn Variational Inequalities: MPEC-View

A scalar Allen-Cahn-MPEC problem is considered and a penalization technique is applied to show the existence of an optimal control. We show that the stationary points of the penalized problems converge to some stationary points of the limit problem, which however are weaker than C-stationarity conditions.