Global solution approaches in equilibrium and stability analysis using homotopy continuation in the complex domain

Comparative study of homotopy continuation methods for nonlinear algebraic equations

“…All of these methods will be discussed in the next section. Jalali et al [10] extended the study of [3] to include equilibrium and stability analysis in the complex domain. Traditionally, a real value initial guess was used to look for real-valued solutions.…”

“…[3][4][5][6][7][8][9][10] and less work on the system of nonlinear algebraic equations i.e. [1][2]11].…”

“…Traditionally, a real value initial guess was used to look for real-valued solutions. In [10], they used an auxiliary function in the complex plane, viz…”

Phase Stability and Equilibrium Calculations in Reactive Systems Using Differential Evolution and Tabu Search

“…Many optimization methods have been tried for stability calculations in reactive systems using the classical tangent plane criterion (e.g. Gupta et al, 1991;Stateva and Wakeham, 1997;Jalali and Seader, 1999;Jalali et al, 2008). Traditional approaches, which generally utilize different initial estimates and local search methods, may converge to a local or trivial solution based on the initial guess.…”

“…Classical thermodynamics indicates that minimization of the Gibbs free energy is a natural approach for calculating the equilibrium state of a mixture. Most of the available methods for Gibbs free energy minimization in reactive mixtures have been proposed during the last two decades, and they include a variety of problem formulations and numerical techniques such as local search methods with and without decoupling strategies (Castillo and Grossmann, 1981;Castier et al, 1989;Xiao et al, 1989;Gupta et al, 1991;Perez-Cisneros et al, 1997;Stateva and Wakeham, 1997), branch-and-bound optimization methods (McDonaldand Floudas, 1996;McKinnon and Mongeau, 1998), algorithms using homotopy continuation (Jalali and Seader, 1999;Jalali et al, 2008), deterministic methods based on interval mathematics (Burgos-Solorzano et al, 2004) and stochastic optimization methods (Reynolds et al, 1997;Lee et al, 1999;Bonilla-Petriciolet et al, 2006;Bonilla-Petriciolet et al, 2008).…”