Linear programming and Simplex--Learning notes __ Math-related

What is a simple shape.

is a general algorithm for solving linear programming problems.
Time complexity compared to metaphysics, not polynomial algorithm, but the actual performance is good. Pre-placement knowledge Linear Programming

Given limited resources and competition constraints, to maximize or minimize a target, if the target can be described as a linear function of some objective, and constrained to some inequalities or equations of some variables, then we can get a linear programming problem , such as the network flow problem is a special linear programming.

Linear programming expressions for several classical problems:

Shortest circuit:
Max: DT Max: d_t
Satisfy constraints: dv<=du+w (U,V) satisfies constraints: D_v
Ds=0,di≥0 D_s=0,\quad D_i\ge 0

Maximum flow:
Maximizing: ∑v∈vflowsv−∑v∈vflowvs maximization: \sum_{v\in v}flow_{sv}-\sum_{v\in V}flow_{vs}
Satisfying constraints: Flowuv≤cap (U,V) satisfies constraints: Flow_{uv}\le cap (U,V)
∑v∈vflowvu=∑v∈vflowuv \sum_{v\in v}flow_{vu}=\sum_{v\in V}flow_{uv}
Fuv≥0 F_{uv}\ge 0
Minimum cost maximum flow:
Minimize: ∑ (u,v) cost (U,V) F