Minimalism Notes

This is a sample of our (approximately) 4 page long Minimalism notes, which we sell as part of the Mathematical Programming Notes collection, a 1st Class package written at LSE in 2011 that contains (approximately) 42 pages of notes across 10 different documents.

Minimalism Revision

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Lecture 4: Minimisation 27 October 2010

Topics

• Minimising and the optimal contour

• Derived constraints

• Optimality

• ≤ and = constraints

• Summary of the y variables when minimising

• To solve a minimisation linear program

• Multiple optimal and unbounded solutions

Key Points

• Feasible region for minimisation problem

• Dual values for minimisation problems

• Converting to maximisation problem

• Solving minimisation problems directly

• Multiple optimal solutions

• Unbounded solutions

Minimising and the Optimal Contour

• With minimisation, all feasible regions lie in the area defined by a greater than or equal inequality

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

Definitions

• Unbounded Solution = When the objective function can increase to infinity

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