Lecture 4&5 - Linear Programming (LP)

Resources - 13.1-13.5 page=377

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The standard form of a linear programming problem is

$$\underset{x\in {\mathbb{R}}^n}{\min }{c}^{T}x,s.t.\{\begin{array}{l}Ax=b\\ x\ge 0\end{array}$$

Transforming a Linear Programming Problem Into Standard Form

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Lecture 4: Common Vector Norms (p-norms) Null Space Range Space Fundamental Theorem of Linear Algebra LU Decomposition Condition Number Properties of Linear Programming Problems The Dual LP Problem Sensitivity

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Lecture 5: Simplex Method The Fundamental Theorem of Linear Programming Basic Feasible Point (BFP) Basic Optimal Point (BOP) Degeneracy

Geometry of the feasible set