Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Comments, with reply on 'Continuous time relay-controlled model reference adaptive-system' by A. Abdulkareem and R. Nagarajam

An adaptive scheme is shown by the authors of the above paper (ibid. vol. 71, no. 2, pp. 275-276, Feb. 1983) for continuous time model reference adaptive systems (MRAS), where relays replace the usual multipliers in the existing MRAS. The commenter shows an error in the analysis of the hyperstability of the scheme, such that the validity of this configuration becomes an open question.

A note on KKT-invexity in nonsmooth continuous-time optimization

We introduce the notion of KKT-inverity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Longitudinal categorical data analysis: A continuous -time Markov chain approach

In this dissertation, we propose a continuous-time Markov chain model to examine the longitudinal data that have three categories in the outcome variable. The advantage of this model is that it permits a different number of measurements for each subject and the duration between two consecutive time points of measurements can be irregular. Using the maximum likelihood principle, we can estimate the transition probability between two time points. By using the information provided by the independent variables, this model can also estimate the transition probability for each subject. The Monte Carlo simulation method will be used to investigate the goodness of model fitting compared with that obtained from other models. A public health example will be used to demonstrate the application of this method. ^

Land Surface Temperature continuous time series from SSM/I passive microwave radiometers, over northern latitudes (Latitudes > 45°N), during summer snow free period (2000-2011), with links to NetCDF files

Remote sensing instruments are key players to map land surface temperature (LST) at large temporal and spatial scales. In this paper, we present how we combine passive microwave and thermal infrared data to estimate LST during summer snow-free periods over northern high latitudes. The methodology is based on the SSM/I-SSMIS 37 GHz measurements at both vertical and horizontal polarizations on a 25 km × 25 km grid size. LST is retrieved from brightness temperatures introducing an empirical linear relationship between emissivities at both polarizations as described in Royer and Poirier (2010). This relationship is calibrated at pixel scale, using cloud-free independent LST data from MODIS instruments. The SSM/I-SSMIS and MODIS data are synchronized by fitting a diurnal cycle model built on skin temperature reanalysis provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The resulting temperature dataset is provided at 25 km scale and at an hourly time step during the ten-year analysis period (2000-2011). This new product was locally evaluated at five experimental sites of the EU-PAGE21 project against air temperature measurements and meteorological model reanalysis, and compared to the MODIS LST product at both local and circumpolar scale. The results giving a mean RMSE of the order of 2.2 K demonstrate the usefulness of the microwave product, which is unaffected by clouds as opposed to thermal infrared products and offers a better resolution compared to model reanalysis.

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

Fault isolation schemes for a class of continuous-time stochastic dynamical systems

In this paper a new method for fault isolation in a class of continuous-time stochastic dynamical systems is proposed. The method is framed in the context of model-based analytical redundancy, consisting in the generation of a residual signal by means of a diagnostic observer, for its posterior analysis. Once a fault has been detected, and assuming some basic a priori knowledge about the set of possible failures in the plant, the isolation task is then formulated as a type of on-line statistical classification problem. The proposed isolation scheme employs in parallel different hypotheses tests on a statistic of the residual signal, one test for each possible fault. This isolation method is characterized by deriving for the unidimensional case, a sufficient isolability condition as well as an upperbound of the probability of missed isolation. Simulation examples illustrate the applicability of the proposed scheme.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.