North-West / Least cost / VAM solution for optimization
Here recommending the nice Youtube video https://youtu.be/ItOuvM2KmD4
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What is Linear combination?
The concept of Linear combination is simple that you already learnt to find the 'X' value from the equation. ex. y = aX +b When you replace 'b' with 'X2' then it will be: y = aX + X2 When you add another constant value for 'X2' with c then: y = aX + cX2 Finally you have two constant values 'a' and 'c' which weight to 'X' and 'X2'. Hence Linear combination is you multiply the constant values ('a', 'c') with Xs and you sum them. Like below. x(t) = ax1(t) + bx2(t) To know more Vector combination with this Click .
Primal problem and Dual problem
When we face the problem that can be solved by the linear problem method, there will be provided two approaches solving the issues called first 'Primal problem' and second is 'Dual problem'. These two methods can be always introduced together against the problem. However it can different results and we call it 'Duality gap'. Primal problem is the original problem given. Dual problem is converted from the original by 'Lagrangian dual problem', 'Wolfe dual problem' or 'Fenchel dual problem'. As usual method 'Lagrangian dual problem' introduces a variable (gamma) having the positive value in order to add the equation into the object function and formulize it as Lagrangian format. And find the minimal value of Dual problem to find the solution of Primal problem. The result value of Primal and Dual problem can be different and we call it 'Duality gap'. Duality gap is always non-negative or zero. References http://m...
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