Optimization is one of the most powerful tools in process integration. Optimization involves the selection of the best solution from among the set of candidate solutions. The degree of goodness of the solution is quantified using an objective function (e.g., cost) which is to be minimized or maximized. The search process is undertaken subject to the system model and restrictions which are termed constraints. Hence, the purpose of optimization is to maximize ( or minimize) the value of a function (called objective function) subject to a number of restrictions (called constraints). These constraints are in the form of equality and inequality expressions. Examples of equality constraints include material and energy balances, process modeling equations, and thermodynamic requirements. On the other hand, the nature of inequality constraints may be environmental (e.g., the quantity of certain pollutants should be below specific levels), technical (e.g., pressure, temperature or flowrate should not exceed some given values) or thermodynamic (e.g., the state of the system cannot violate second law of thermodynamics). The principles of optimization theory and algorithms are covered by various books (e.g., Diwekar 2003; Tawarmalani and Sahinidis 2003; Floudas and Pardalos, 2001; Edgar and Himmelblau 2001; Floudas 1999; Grossmann 1996). Additionally, for a retrospective and future prospective on optimization, the reader is referred to recent publications (e.g., Biegler and Grossmann 2005; Grossmann and Biegler 2005; Floudas et al., 2004). This chapter presents an overview of using mathematical techniques to formulate optimization problems. Additionally, the use...