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The usability of the scenario theory, however, has been restrained thus far by the obstacle that most results are standing on the <jats:italic>assumption of convexity<\/jats:italic>. With this paper, we aim to free the theory from this limitation. Specifically, we focus on the body of results that are known under the name of \u201cwait-and-judge\u201d and show that its fundamental achievements maintain their validity in a <jats:italic>non-convex<\/jats:italic> setup. While optimization is a major center of attention, this paper travels beyond it and into <jats:italic>data-driven decision making<\/jats:italic>. Adopting such a broad framework opens the door to building a new theory of truly vast applicability.<\/jats:p>","DOI":"10.1007\/s10107-024-02074-3","type":"journal-article","created":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T13:01:42Z","timestamp":1712581302000},"page":"557-608","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Non-convex scenario optimization"],"prefix":"10.1007","volume":"209","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5451-6892","authenticated-orcid":false,"given":"Simone","family":"Garatti","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5209-3312","authenticated-orcid":false,"given":"Marco C.","family":"Campi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,4,8]]},"reference":[{"key":"2074_CR1","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611975444","volume-title":"Introduction to the Scenario Approach","author":"MC Campi","year":"2018","unstructured":"Campi, M.C., Garatti, S.: Introduction to the Scenario Approach. 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