Learn Russian: Компания использует этот капитал с целью внедрить новый алгоритм. - The company uses this capital with the aim of implementing a new algorithm.

с целью translates to 'with the aim of' or 'with the purpose of' and belongs to a formal, business, or academic register. While чтобы would be grammatically correct, с целью fits much better with corporate vocabulary like капитал and внедрить.

Can we use с целью plus an infinitive if the subjects of the two actions are different?

No. Because the company is doing both actions (using capital and implementing), we can use с целью followed directly by the infinitive внедрить. If a different entity were implementing it, you would have to use a verbal noun instead, such as с целью внедрения.

Why is the perfective verb внедрить used instead of its imperfective counterpart внедрять?

The company's goal is the successful, completed integration of the algorithm. In purpose clauses, using the perfective aspect emphasizes achieving that final result, rather than just the ongoing process of working on it.

What is the exact nuance of the verb внедрить?

It specifically means to implement, introduce, or embed something into an existing system or workflow. You will often see it used in business and tech contexts for rolling out new software, policies, or, as in this sentence, an алгоритм.

Why does look like it is in the nominative case if it is the direct object?