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A known idea is that constant-rank type CQs allow one to modify the description of the feasible set, by eliminating redundant constraints, so that the Mangasarian-Fromovitz CQ (MFCQ) holds. Traditionally, such modifications, called\n                    <jats:italic>reductions<\/jats:italic>\n                    here, have served primarily as auxiliary tools to connect existing CQs. In this work, we adopt a different viewpoint: we treat the very existence of such reductions as a CQ in itself. We study these \u201creduction-induced\u201d CQs in a general framework, relating them not only to MFCQ, but also to arbitrary CQs. Moreover, we establish their connection with the local error bound (LEB) property. Building on this, we introduce a relaxed variant of the constant rank CQ known as\n                    <jats:italic>constant rank of the subspace component<\/jats:italic>\n                    (CRSC). This new CQ preserves the main geometric features of CRSC, guarantees LEB and the existence of reductions to MFCQ.\n                  <\/jats:p>","DOI":"10.1007\/s10957-026-02965-9","type":"journal-article","created":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T04:20:15Z","timestamp":1774498815000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Constant-Rank-Type Condition Related to MFCQ and Local Error Bounds"],"prefix":"10.1007","volume":"209","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2031-4325","authenticated-orcid":false,"given":"Roberto","family":"Andreani","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9340-3372","authenticated-orcid":false,"given":"Mariana da","family":"Rosa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9224-9051","authenticated-orcid":false,"given":"Leonardo D.","family":"Secchin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,26]]},"reference":[{"key":"2965_CR1","unstructured":"Abadie, J.: On the Kuhn-Tucker theorem. 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