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Minimalism Notes

Operational Research Notes > Mathematical Programming Notes

This is an extract of our Minimalism document, which we sell as part of our Mathematical Programming Notes collection written by the top tier of LSE students.

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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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