how to solve this kind of optimization problem

Hi, there.

I wish I can find some help in this forum.

First I have an optimization problem as follows.

min f(x[1], x[2], x[3], x[4],..., x[99], x[100])
s.t. h(x[1], x[2], x[3], x[4],..., x[99], x[100]) = 0;
g-<g(x[1], x[2], x[3], x[4],..., x[99], x[100]) <g+;
x-<x[i]<x+, i =1, 2, 3,..., 100;

This can be solved by interior-point method.

However suppose that there is a new constraint on x now.
sum(k(x[i],x[i+1]))<=50; i = 1, 2, 3,...99;
where k(x[i],x[i+1])=0 if x[i]~=x[i+1] and k(x[i],x[i+1])=0 if
x[i]==x[i+1]

The physical meaning of this new constraint is that we expect the
change on x[i] is less than a constaint value, which is 50 in this
example.

How to deal with this new constraint? Can this new optimization
problem still be solved by interior point method? Please do me a
favour.

Thanks in advance.

.

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