ABSTRACT

Nonlinear programming problems are divided into two kinds of problems: unconstrained and constrained [19, 20]. An unconstrained optimization problem is a problem of the form min f ( x ) , x = [ x 1 , x 2 , … , x n ] T ∈ R n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/math10_1.jpg"/>

A general constrained optimization problem consists of the objective function in Equation (10.1) with equality constraints: E ( x ) = 0 , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/math10_2.jpg"/> and inequality constraints: I ( x ) ≤ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/math10_3.jpg"/> where x ∈ R n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/inline-math10_1.jpg"/> , E ( x ) ∈ R p https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/inline-math10_2.jpg"/> and I ( x ) ∈ R q https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429021985/fe8daa6e-4e4e-420f-856d-5f69c2393613/content/inline-math10_3.jpg"/> .

In this chapter, methods for solving both unconstrained and constrained optimization problems using MATLAB® and Python will be implemented.