This paper presents an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of Process Design and Control. The focus is on global optimization methods for (a) twice-diierentiable constrained nonlinear optimization problems, (b) mixed-integer nonlinear optimization problems, and (c) locating all solutions of nonlinear systems of equa...

This paper is concerned with chance constrained programming to deal with nonlinear optimization problems with random parameters. Specific Monte Carlo methods to evaluate the gradient and Hessian of probabilistic constraints are proposed and discussed. These methods are implemented in penalization optimization routines adapted to stochastic optimization. They are shown to reduce the computationa...

This paper proposes a constrained nonlinear programming view of generalized autoregressive conditional heteroskedasticity (GARCH) volatility estimation models in financial econometrics. These models are usually presented to the reader as unconstrained optimization models with recursive terms in the literature, whereas they actually fall into the domain of nonconvex nonlinear programming. Our re...

A numerical algorithm for approximate multi-parametric nonlinear programming is developed. It allows approximate solutions to nonlinear optimization problems to be computed as explicit piecewise linear functions of the problem parameters. In control applications such as nonlinear constrained model predictive control this allows efficient online implementation in terms of an explicit piecewise l...

In this paper, we present constrained simulated annealing (CSA), an algorithm that extends conventional simulated annealing to look for constrained local minima of nonlinear constrained optimization problems. The algorithm is based on the theory of extended saddle points (ESPs) that shows the one-to-one correspondence between a constrained local minimum and anESP of the corresponding penalty fu...

Recently primal-dual interior-point methodology has proven to be an eeective tool in linear programming applications and is now being extended, with great enthusiasm to general nonlinear programming applications. The primary purpose of this current study is to develop and promote the belief that since Newton's method is a tool for square nonlinear systems of equations, the fundamental role of i...