Ok, the no.1 interest in India Ocean is: not allow anyone to dominate this area except herself. Now, let's see how you negotiate that.
Thanks for pointing out the inaccuracy in my reading of the Monroe doctrine. I definitely need to brush up on my history.
As for the Indian ocean region, we don't see it from the point of view of exclusivity of access. We see it as an asset which we are willing to share in exchange for other strategic concessions. India has been trying to add another 250 miles to its exclusive economic zone since years, but the US kept refusing it and repeatedly conducted 'freedom of navigation' missions and invading that space, just like they are doing for the South China sea. We didn't raise an alarm because, firstly, we don't have the might to take on the US, secondly, we were willing to use it as a bargaining chip in the future. Just having large swathes of territory and controlling it militarily is no use if nations resort to exclusion as a response to exclusivity and refuse to trade with you. There has to be a balance between our desire to protect the exclusivity of our territory and our need to conduct business. In fact we allow China to enter deep inside the Bay of Bengal and port their ships at Chittagong port (Bengal). We never put any pressure on Bengal to get them to evict the Chinese presence on that port. Instead, we patiently watched as China to build that port in our neighborhood, and once it was inaugurated, we signed a deal with Bangladesh to share access to that port so that even Indian ships can use it.
At a military level, controlling the Indian ocean and correspondingly defending it lies in the two choke points, one is strait of Malacca and another is strait of Hormuz. The fact remains that ever regional power has the capability to choke these. The only thing that stops them is the bilateral trade with India, and their multilateral trade with other south Asian nations that would be affected. As per game theory, they would be committing suicide, since it is in everyone's mutual interest to keep the trade flowing, especially considering the global slowdown which is causing joblessness, which might exacerbate riots in many nations, if trade is stopped. We don't want to dominate the Indian ocean region, we are willing to share access; We simply don't want anyone else to dominate the area and so we work with regional partners to ensure this status quo is maintained.
If it comes to just keeping foreign naval missile launch platforms away from our shores, we have achieved that capability already. We also have other pressure points (economic and diplomatic). Take for example the recent Pathankot attack where our NSA cancelled his meeting with the Chinese NSA. This jeopardizes Chinese strategic calculations in the region because China is itching to buy temporary peace with India to engage with other, more pressing issues like the south China sea. So, we are willing to inflict retribution onto the backers of Pakistan if this continues. There is also a possibility of multinational military drills in addition to the Naval drills (US, India, Japan) that we already did. If Pakistan keeps needling us, we start needling China. If US sends military aid to Pakistan, we join the Russia-led alliance on Syria. As long as disagreeing with India entailed no adverse strategic implications, it was considered alright to tick off India. They will learn soon that there is a cost to pay if you disagree with us.
As for Pakistan, we have other ways of avenging the deaths of our people while keeping the conflict below the nuclear threshold. There is complete consolidation of public opinion in India vis-a-vis Pakistan. The political authority knows that there is popular support for retribution and they will handle it appropriately. Not every altercation turns nuclear.
