uf_subproblem

Solve the sub-optimization problem in distributed algorithm for user friendly problem

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Description

uf_subproblem solves the sub-optimization problem assigned for each charger during the distributed algorithm for user friendly problem. This function is only for the function user_friendly.

Syntax

[xi,optval] = uf_subproblem(T,l,x,d,P_max,P_min,A,b,empty_ind,G,h,cs,pc1,pc2,pc3,bs,c,rho)

Input Arguments

Name	Type	Description
T	positive integer	Number of time slots comprising a scenario
l	(2T)×1 vector	Variable for building the cost function
x	(3T)×1 vector	Variable for building the cost function
d	(2T)×1 vector	Variable for building the cost function
P_max	nonnegative scalar	Maximum aggregate charging power
P_min	nonpositive scalar	Minimum aggregate charging power
A	T×T matrix	Local constraint matrix
b	T×1 vector	Local constraint matrix
empty_ind	T×1 vector	Index for empty time slot (for one charger)
G	matrix	Penalty matrix
h	vector	Penalty matrix
cs	1×T vector	Vector for calculating (cost saving) cost function
pc1	1×T vector	Vector for calculating (priority charging) cost function
pc2	T×1 vector	Vector for calculating (priority charging) cost function
pc3	T×T matrix	Matrix for calculating (priority charging) cost function
bs	1×T vector	vector for calculating (battery saving) cost function
c	positive scalar	Parameter for optimization algorithm
rho	nonnegative scalar	Penalty parameter

Output Arguments

Name	Type	Description
xi	(3T)×1 vector	Optimal solution of the subproblem
optval	scalar	Optimal value