Zinc is the first modelling language which supports solver and technique independence. This means that a high level conceptual model can be automatically mapped into an appropriate low level design model for a specific solver or technique. To date, Zinc uses three different techniques to solve a model: Constraint Programming (CP), Local Search (LS), and Mixed Integer Programming (MIP). In this way, modellers can examine all solving techniques for their models and see which one gives them the best result. MIP solvers can only accept linear models. Therefore, to map a conceptual model to MIP solvers, the model must be linearized first. In this paper we explain the techniques used in Zinc to linearize high level data structures and expressions which may be appeared in a conceptual model. As a result, modellers can benefit of expressive modelling using nonlinear expressions as well as efficiency of MIP solvers.

pH control is a challenging problem due to its highly nonlinear nature. In this paper the performances of two different adaptive global linearizing controllers (GLC) are compared. Least squares technique has been used for identifying the titration curve. The first controller is a standard GLC based on material balances of each species. For implementation of this controller a nonlinear state estimator is used. Some modifications are proposed to avoid the singularity of the observer gain. The second controller is designed based on the reduced state equation. Through computer simulations, it has been shown that the performances of the second GLC is superior and it is more robust to process model mismatch. It should be also noted that the design of reduced state-based GLC is much easier and dose not need observer for implementation.

Tail equivalent Linearization method is based on first order reliability method, which obtains an equivalent linear system for the considered nonlinear problemwith equal tail probability related to a specified threshold and time. This method has been applied only to nonlinear non-degrading single- and multi-degrees of freedom shear beam twodimensional models and three-dimensional one-story rigid diaphragm supported by frames with in-plane uni-axial stiffness which is subjected to independent random excitation along the structural axes. To use TELM for more practical problems it is required to extend this method to cover more realistic material and excitation characteristics. In this paper, some of these developments have been presented. Application of TELM for bi-directional excitation with bi-axial material subjected to different incidence angles of excitation and using TELMfor degrading material which has been presented in the previous works of the authors have been reviewed briefly. In addition a new method for defining rotational dependent component of earthquake excitation in terms of independent translational components in the standard normal random variable space is proposed, and TELM has been used for this kind of excitation. Three examples related to these extensions have been presented; the comparison of the TELM results with Mote-Carlo simulation results shows good agreement.

In this paper, multiobjective optimization problems with nondifferentiable quasiconvex functions are considered. We obtain some duality results and a linear representation for the considered problems. Since the well-known strong duality result is not valid for the problems, we present a weaker form of it, named quasi-strong duality result.