Research topic for optimisation

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I am an undergraduate student in computer science with a strong inclination towards mathematics. I want to do some research work under my mathematics Professor who specialises in Optimisation related techniques. So, I want to ask what are some research topics in optimisation with which I can approach my professor? I want some topics on which I can work upon without prior deep knowledge about them. I will grateful for your help.

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Operations research is one suggestion. I would investigate the possible applications and pick one you have an interest in or a passion for. An interesting and useful hot topic would be to research the current US healthcare system.