Can intentionally omitting related work (citations) be considered as misconduct?

I've seen a recent journal paper that presents a solution to a problem, and it in the introduction it has a statement that the problem has not been solved yet. That wouldn’t be very strange if I didn’t publish a paper with a solution a few years ago, which is not cited.

I understand that no one can be aware of all papers published so there can be honest omissions, but these authors were aware of my paper because we talked about it at a conference held before the submission of their paper.

Another case which I have noticed is that some papers avoid mentioning other related papers which present similar methods but perform better than theirs.

Is this considered as misconduct, and is there something one can do about it?

Answer

Yes. If they were indeed aware of the fact that a paper exists which proves that the problem was solved, then they clearly commited a scientific misconduct, though less so, I should think, by not citing your paper, and more so by claiming that a problem had no solution which they knew was solved already. Even if they considered your proof wrong, they should absolutely make it clear why they disagree with you.

However, as commenters have pointed out, there is always a good chance that people don't realise what a paper is about, don't remember that there is that paper, or they wanted to discuss your paper and just forgot about it, which of course doesn't speak for their academic diligence, but means that no misconduct was commited (unless your paper is so high-profile that by not including it, they are neglecting their duty to read the literature before writing a paper.)

Edit: Note that I have answered the general question in your title, not the more precise question in your text, which I don't know how to answer without additional evidence.

Another edit: The formal rules for scientific integrity of my own university, for example, do not explicitly mention omitting a citation, but do (obviously) contain "intentional or grossly negligent misrepresentations in an academically relevant context" (my translaton) as an act of misconduct. This is exactly my point: If they knew, or really should have known, it's academic misconduct. If they didn't know and your paper is so obscure that they didn't act grossly negligent in not finding it, it isn't.