This survey covers the state of the art of techniques for solving general purpose constrained global optimization problems and continuous constraint satisfaction problems, with emphasis on complete techniques that provably nd all solutions (if there are nitely many). The core of the material is presented in sucient detail that the survey may serve as a text for teaching constrained global optimization.

University for instruction in the language and principles of chemical engineering, many consultations and much useful advice. Appreciation is also due to the referees, whose comments on an earlier version of the paper have been invaluable. Summary. We propose a new method for estimating parameters in non-linear differential equations. These models represent change in a system by linking the behavior of a derivative of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to statistical techniques such as inference and interval estimation. This paper describes a new method that uses noisy data to estimate the parameters defining a system of nonlinear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive interval estimates and show that these have good coverage properties on data simulated from chemical engineering and neurobiology. The method is demonstrated using real-world data from chemistry and from the progress of the auto-immune disease lupus. Keywords: Differential equations, profiled estimation, estimating equations, Gauss-Newton

This paper presents an approach for the global optimization of constrained nonlinear programming problems in which some of the constraints are non-analytical (non-factorable), defined by a computational model for which no explicit analytical representation is available.

this paper we extend these thoughts to the regression analysis scenario. Preliminary experimental results are presented for which the optimal kernel matrix for support vector machine regression is retrieved

University for instruction in the language and principles of chemical engineering, many consultations and much useful advice. Appreciation is also due to the referees, whose comments on an earlier version of the paper have been invaluable. Summary. We propose a new method for estimating parameters in models de ned by a system of non-linear differential equations. Such equations represent changes in system outputs by linking the behavior of derivatives of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation. This paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters de ning a system of nonlinear differential equations. The approach is based on a modi cation of data smoothing methods along with a generalization of pro led estimation. We derive estimates and con dence intervals, and show that these have low bias and good coverage properties, respectively, for data simulated from models in chemical engineering and neurobiology. The performance of the method is demonstrated using real-world data from chemistry and from the progress of the auto-immune disease lupus.