Linear programming for optimal separation between points

Hello I've got following problem to solve So what I have to do is find optimal times t(i) for set of n times, that ensures that every member of the set t(i) is within bonds t_lb(i) and t_up(i) and is separated from other members with time t_sep. The objective is to minimuze the difference between expected time t0(i) and calculated time t(i). I written this problem mathematically as:

Constants:

t_lb, t_up, t0

Constrains:

t_lb(i) < t(i) < t_up(i)
abs(t(i) - t(j)) > t_sep %for every j different than i

Objective:

sum(t(i)-t0(i))

But I dont know how to employ this in Matlab. Many thanks for the help :)

Answer 1

[Torsten]

Use MATLAB's "intlinprog" and read

http://lpsolve.sourceforge.net/5.1/absolute.htm

on how to resolve the abs(t(i)-t(j))> t_sep condition.

Best wishes

Torsten.

[Adr Paw]

Hey thank you so much for the answer. I will try to solve this next week and post here if I succedd :)