ABSTRACT
In this chapter, multi-objective optimization problems (MOPs) of nonlinear algebraic systems are introduced. Some properties of MOPs are given first. Based on local linearized systems, the MOP of nonlinear algebraic systems can be transformed into linear matrix inequality (LMI)–constrained MOP. Based on the conventional multi-objective evolution algorithm (MOEA), a reverse-order LMI-constrained MOEA is also introduced to solve LMI-constrained MOPs. Finally, a numerical simulation example is also provided for solving a LMI-constrained MOP of nonlinear algebraic systems to illustrate the design procedure and validate the proposed multi-objective optimization method. These results of MOPs of nonlinear algebraic systems can be easily extended to the MOPs of nonlinear stochastic systems in the following chapters.
