It is well-known that asymptotic stability (AS) of homogeneous polynomial vector fields of degree one (i.e., linear systems) can be decided in polynomial time e.g. by searching for a quadratic Lyapunov function. Since homogeneous vector fields of even degree can never be AS, the next interesting degree to consider is equal to three. In this … Read more
The multilinear least-squares (MLLS) problem is an extension of the linear least-squares problem. The difference is that a multilinear operator is used in place of a matrix-vector product. The MLLS is typically a large-scale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present … Read more
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more
We introduce the framework of path-complete graph Lyapunov functions for approximation of the joint spectral radius. The approach is based on the analysis of the underlying switched system via inequalities imposed among multiple Lyapunov functions associated to a labeled directed graph. Inspired by concepts in automata theory and symbolic dynamics, we define a class of … Read more
We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only … Read more
All manifestations of dimensional harmony in nature and human practice are being always characterized by deviations from golden ratio that often makes their acceptance problematic. On the example of Fechner’s experiments the paper discusses the way of solving this problem, based on informational approach, according to which the informatively optimal permissible deviation from dimensional harmony … Read more
We study a class of linear programming (LP) problems motivated by large-scale machine learning applications. After reformulating the LP as a convex nonsmooth problem, we apply Nesterov’s primal-dual smoothing technique. It turns out that the iteration complexity of the smoothing technique depends on a parameter $\th$ that arises because we need to bound the originally … Read more
We relate a deterministic Kalman filter on semi-infinite interval to linear-quadratic tracking control model with unfixed initial condition Citation Technical report, University of Notre Dame, October, 2011 Article Download View Deterministic Kalman Filtering on Semi-infinite Interval
The conception of dimensional perfection and based on principles of qualimetry and information theory the criterion of informational optimality have been used for analyzing modeling functions of measurement. By means of variances of uncertainty contributions, transformed into their relative weights, the possibility of determining informatively rational and optimal levels of confidence for expanded uncertainty has … Read more
This paper provides a new multi-objective integer programming model for the daily scheduling of nurses in operating suites. The model is designed to assign nurses to di erent surgery cases based on their specialties and competency levels, subject to a series of hard and soft constraints related to nurse satisfaction, idle time, overtime, and job changes … Read more