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MAS aims to optimize a deterministic function over a box-bounded domain and is designed to work well within a confined budget of function evaluations. In MAS, the search is oriented to improve the value of the incumbent by combining a set of techniques, including gradient estimation and quadratic model building and optimization. We propose a novel sensitivity-based approach to construct an incomplete quadratic model when points are not enough to build a complete quadratic surrogate model of the true function. The surrogate model is then used to guide the search. We present extensive computational results on a collection of 501 publicly available test problems with varying dimensions and complexity. The computational results demonstrate that MAS performs well regardless of problem convexity and smoothness.\n                  <\/jats:p>","DOI":"10.1007\/s10589-025-00686-9","type":"journal-article","created":{"date-parts":[[2025,5,11]],"date-time":"2025-05-11T10:32:02Z","timestamp":1746959522000},"page":"889-921","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Model-and-search: a derivative-free local optimization algorithm"],"prefix":"10.1007","volume":"92","author":[{"given":"Kaiwen","family":"Ma","sequence":"first","affiliation":[]},{"given":"Luis Miguel","family":"Rios","sequence":"additional","affiliation":[]},{"given":"Hua","family":"Zheng","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2087-9131","authenticated-orcid":false,"given":"Nikolaos V.","family":"Sahinidis","sequence":"additional","affiliation":[]},{"given":"Sreekanth","family":"Rajagopalan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,11]]},"reference":[{"key":"686_CR1","unstructured":"Abramson, M.A., Audet, C., Couture, G., Dennis, Jr., J.E., Le\u00a0Digabel, S.: The Nomad project (Current as of 9 January 2025). https:\/\/www.gerad.ca\/en\/software\/nomad\/"},{"key":"686_CR2","unstructured":"Adams, B.M., Ebeida, M.S., Eldred, M.S., Geraci, G., Jakeman, J.D., Maupin, K.A., Monschke, J.A., Stephens, J.A., Swiler, L.P., Vigil, D.M., Wildey, T.M., Bohnhoff, W.J., Dalbey, K.R., Eddy, J.P., Frye, J.R., Hooper, R.W., Hu, K.T., Hough, P.D., Khalil, M., Ridgway, E.M., Winokur, J.G., Rushdi, A.: DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 6.9 User\u2019s Manual. 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