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The goal is to perform an efficient material parameter identification knowing the elastic displacement field induced by a mechanical load. We propose to define the inverse problem through a quadratic optimization program which uses the direct problem formulation to define the objective function. In this way, we end up with a convex minimization problem which attains its minimum at the solution of a linear system. The effectiveness of our method is illustrated through numeral examples.<\/jats:p>","DOI":"10.1186\/s13362-024-00156-7","type":"journal-article","created":{"date-parts":[[2024,8,19]],"date-time":"2024-08-19T10:02:57Z","timestamp":1724061777000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A quadratic optimization program for the inverse elastography problem"],"prefix":"10.1186","volume":"14","author":[{"given":"S\u00edlvia","family":"Barbeiro","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4173-8469","authenticated-orcid":false,"given":"Rafael","family":"Henriques","sequence":"additional","affiliation":[]},{"given":"Jos\u00e9 Luis","family":"Santos","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,19]]},"reference":[{"key":"156_CR1","doi-asserted-by":"crossref","unstructured":"Ainsworth M, Parker C. Unlocking the secrets of locking: Finite element analysis in planar linear elasticity. Comput Methods Appl Mech Eng. 2022;395.","DOI":"10.1016\/j.cma.2022.115034"},{"key":"156_CR2","series-title":"Proceedings of the 22nd ECMI conference on industrial and applied mathematics","volume-title":"The derivative free trust-region method for the inverse elastography problem","author":"S Barbeiro","year":"2023","unstructured":"Barbeiro S, Henriques R, Santos J. The derivative free trust-region method for the inverse elastography problem. Proceedings of the 22nd ECMI conference on industrial and applied mathematics. 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