In optimization world, what is the definition of an admissible solution? This word admissible solution appears in many papers, but I cannot find any definition of it. For example, in the paper "GLOBAL OPTIMIZATION WITH POLYNOMIALS AND THE PROBLEM OF MOMENTS∗"
2026-03-25 07:40:39.1774424439
What is an admissible solution
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In optimization framework, usually we work in a "big" set $X$ (a Banach space for example) but sometimes we need a solution that satisfies some conditions (Constraints, Regularity, ... etc). So, we have to restrict ourselves to a subset $U_{\mathrm{ad}} \subset X$ called the set of admissible solutions. That is the set that we optimize our functional on it. An admissible solution means that it should belongs to $U_{\mathrm{ad}}$ and a solution which is just in $X$ is not enough.