ABSTRACT
This chapter includes some discussion of computational aspects. The theoretical analysis for non-linear optimisation is based on calculus. The chapter explores the complications of constrained optimisation, non-negativity requirements, and variables that are not restricted as to sign, but are subject to equality constraints. It considers optimisation of non-negative variables subject to equality constraints. Apart from the linear model there are some other cases where this property holds. The chapter discusses the analysis that is extended to the case of non-negative variables and inequality constraints. It introduces the concepts of local and global optima, and it was remarked there that, in the linear model, a local optimum is always a global optimum. The technique for handling non-negative variables may now be combined with the Lagrange multiplier method for dealing with equality constraints. In economic applications, the constraints are commonly inequalities rather than equalities, and thus it is important to be able to extend the previous analysis.
