### Minimalism Notes

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### Minimalism Revision

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Lecture 4: Minimisation
27 October 2010

Topics Key Points
• Minimising and the optimal contour • Feasible region for minimisation problem
• Derived constraints
• Dual values for minimisation problems
• Optimality
• ≤ and = constraints • Converting to maximisation problem
• Summary of the y variables when minimising • Solving minimisation problems directly
• To solve a minimisation linear program • Multiple optimal solutions
• Multiple optimal and unbounded solutions • Unbounded solutions

Definitions
Minimising and the Optimal Contour
• Unbounded Solution = When the objective
• With minimisation, all feasible regions lie in the area defined by a greater than or equal inequality
function can increase to infinity

At the optimum point, all the feasible
region lies in the area defined by

Derived Constraints
• If we have a uniform set of inequalities, then we can add together non-negative multiples of them to derive
a new valid inequality
○ The feasible area of the new inequality includes the feasible area defined by the original ones
• We use matrices for when we have more than 2 inequalities

Optimality
• We follow the same procedure as with maximisation to determine feasibility and optimality
• See Lecture 3: Optimality for more details

Course Notes Page 5

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