Best ways to resolve the problems in Relationship,

Dear all,
according to you what are the best ways to resolve when you have below problematic elements in your relationship:

1-Strong difference of opinions and difference in self believes and thought process.
2- when the partners are having strong ideological differences and dis-ability to get convince and change for his and her partner.
3- Ego problem as I am right and you are wrong.

Looking forward for your valuable suggestions and thoughts sharing,,,