Abstract-We consider an optimizing process (or parametric optimization problem), i.e., an optimization problem that depends on some parameters. We present a method for imputing or estimating the objective function, based on observations of optimal or nearly optimal choices of the variable for several values of the parameter, and prior knowledge (or assumptions) about the objective. Applications include estimation of consumer utility functions from purchasing choices, estimation of value functions in control problems, given observations of an optimal (or just good) controller, and estimation of cost functions in a flow network.

A wireless sensor network employing multiple sensing and event detection modalities and distributed processing is proposed for smart home monitoring applications. Image sensing and vision-based reasoning are employed to verify and further analyze events reported by other sensors. The system has been developed to address the growing application domain in caregiving to the elderly and persons in need of monitored living, who care to live independently while enjoying the assurance of timely access to caregivers when needed. An example of sensed events is the accidental fall of the person under care. A wireless badge node acts as a bridge between the user and the network. The badge node provides user-centric event sensing functions such as detecting falls, and also provides a voice communication channel between the user and the caregiving center when the system detects an alert and dials the center. The voice connection is carried over an IEEE 802.15.4 radio link between the user badge and another node in the network that acts as a modem. Using signal strength measurements, the network nodes keep track of the approximate location of the user in the monitoring environment. The network also includes wall-mounted image sensor nodes, which are triggered upon detection of a fall to analyze their field-of-view and provide the caregiving center with further information about the user's status. A description of the developed network and several examples of the vision-based reasoning algorithm are presented in the paper.

Abstract-This paper considers moving horizon estimation (MHE) approach to solution of staged quadratic programming (QP) problems. Using an insight into the constrained solution structure for the growing horizon, we develop a very accurate iterative update of the arrival cost in the MHE solution. The update uses a quadratic approximation of the arrival cost and information about the previously active or inactive constraints. In the absence of constraints, the update is the familiar Kalman filter in information form. In the presence of the constraints, the update requires solving a sequence of linear systems with varying size. The proposed MHE update provides very good performance in numerical examples. This includes problems with ℓ1 regularization where optimal estimation allows us to perform online segmentation of streaming data.

SUMMARYWe consider the use of quadratic approximate value functions for stochastic control problems with input‐affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic programming policy in such cases requires the solution of an explicit convex optimization problem, such as a quadratic program, which can be carried out efficiently. We describe a simple and general method for approximate value iteration that also relies on our ability to solve convex optimization problems, in this case, typically a semidefinite program. Although we have no theoretical guarantee on the performance attained using our method, we observe that very good performance can be obtained in practice.Copyright © 2012 John Wiley & Sons, Ltd.