EECM 3714
Lecture 9: Unit 9
Constrained Optimisation
Renshaw, Ch. 16
20 April 2021
,OUTLINE
• Introduction
• The Lagrange multiplier method
• Cost minimisation
• Output maximisation
• Examples
• Utility maximisation
• Examples
, CONSTRAINED OPTIMISATION
• Constrained optimisation involves finding values of the independent variables of a function
minimise/maximise the function, subject to a constraint.
• Suppose that we want to maximise/minimise 𝑓(𝑥, 𝑦) subject to a constraint, 𝑔(𝑥, 𝑦)
• max 𝑓(𝑥, 𝑦), s.t. 𝑔(𝑥, 𝑦)
• min 𝑓(𝑥, 𝑦), s.t. 𝑔(𝑥, 𝑦)
• Where: 𝑓(𝑥, 𝑦) is the objective function (the function to be minimised or maximised); and 𝑔(
is the constraint.
• Fig 16.2, Fig 16.4, Fig 16.5
Lecture 9: Unit 9
Constrained Optimisation
Renshaw, Ch. 16
20 April 2021
,OUTLINE
• Introduction
• The Lagrange multiplier method
• Cost minimisation
• Output maximisation
• Examples
• Utility maximisation
• Examples
, CONSTRAINED OPTIMISATION
• Constrained optimisation involves finding values of the independent variables of a function
minimise/maximise the function, subject to a constraint.
• Suppose that we want to maximise/minimise 𝑓(𝑥, 𝑦) subject to a constraint, 𝑔(𝑥, 𝑦)
• max 𝑓(𝑥, 𝑦), s.t. 𝑔(𝑥, 𝑦)
• min 𝑓(𝑥, 𝑦), s.t. 𝑔(𝑥, 𝑦)
• Where: 𝑓(𝑥, 𝑦) is the objective function (the function to be minimised or maximised); and 𝑔(
is the constraint.
• Fig 16.2, Fig 16.4, Fig 16.5
