{"id":982,"date":"2023-05-25T08:10:47","date_gmt":"2023-05-25T08:10:47","guid":{"rendered":"https:\/\/nag.com\/?page_id=982"},"modified":"2023-07-11T15:42:11","modified_gmt":"2023-07-11T15:42:11","slug":"faster-data-fitting-solver","status":"publish","type":"page","link":"https:\/\/nag.com\/faster-data-fitting-solver\/","title":{"rendered":"Faster Data Fitting Solver"},"content":{"rendered":"\n
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Faster Data Fitting Solver<\/h1>\n \n
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Calibrating the parameters of complex numerical models to fit real-world observations is one of the most common problems found in industries such as finance, physics, simulations, engineering, etc. n<\/i><\/span>AG introduces at Mark\u00a027.1 of the n<\/i><\/span>AG Library a novel nonlinear least squares (NLN-LSQ) trust-region solver\u00a0handle<\/span>_solve<\/span>_bxnl<\/span><\/a>\u00a0(e04gg<\/a>) for unconstrained and bound-constrained fitting problems which implements various algorithms and regularization techniques. It is aimed at small to medium-sized fitting problems (up to 1000s of parameters) of the form<\/p>\n <\/div>\n <\/div>\n\n \n \n

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\"\"<\/p>\n <\/div>\n <\/div>\n\n \n \n <\/div>\n <\/div>\n<\/div>\n\n\n minimize<\/mtext> x<\/mi> \u2208<\/mo> \u211d<\/mi> n<\/mi> <\/msup> <\/mrow> <\/munder> <\/mtd> \u2211<\/mo> i<\/mi> =<\/mo> 1<\/mn> <\/mrow> m<\/mi> <\/munderover> \u03d5<\/mi> (<\/mo> t<\/mi> <\/mrow> i<\/mi> <\/mrow> <\/msub> ,<\/mo> x<\/mi> <\/mrow> )<\/mo> <\/mrow> –<\/mo> y<\/mi> <\/mrow> i<\/mi> <\/mrow> <\/msub> <\/mfenced> 2<\/mn> <\/msup> <\/mstyle> <\/mtd> <\/mtd> <\/mspace> <\/mtd> <\/mtr> subject to<\/mtext> <\/mtd> <\/mspace> \u2113<\/mi> \u2264<\/mo> x<\/mi> \u2264<\/mo> u<\/mi> ,<\/mo> <\/mspace> <\/mtd> <\/mtd> <\/mspace> <\/mtd> <\/mtr> <\/mtable> <\/math>\n\n\n\n
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where the idea is to find optimal values for the parameters, \\(x\\), of the model represented by the smooth function \\(\u03d5(t,x)\\) (blue line) which fit \\(m\\) observed data points \\((t_{i},y_{i})\\) (black dots). That is, to minimize the squared error between the model and the data (vertical red bars).<\/p>\n

e04gg<\/a>\u00a0<\/span>should present a significant improvement over the current nonlinear least squares solvers in the n<\/i><\/span>AG Library. In addition, this solver fills the gap between unconstrained solvers such as\u00a0lsq<\/span>_uncon<\/span>_quasi<\/span>_deriv<\/span>_comp<\/span><\/a>\u00a0<\/span>(e04gb<\/a><\/span>) and the fully constrained ones, such as\u00a0lsq<\/span>_gencon<\/span>_deriv<\/span><\/a>\u00a0<\/span>(e04us<\/a><\/span>).<\/p>\n

e04gg<\/a>\u00a0<\/span>is part of the\u00a0n<\/i><\/span>AG Optimization Modelling Suite<\/a>\u00a0which offers clarity and consistency on the interface of the solvers within the suite.<\/p>\n

The new solver stems from a collaboration with the Rutherford Appleton Laboratory\u00a0[1<\/a>]<\/span>\u00a0and demonstrates n<\/i><\/span>AG\u2019s ongoing effort to expand and improve its offering in mathematical optimization.<\/p>\n <\/div>\n <\/div>\n<\/div>\n\n\n

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<\/div>\n\n \n Try the solver <\/i><\/a> <\/div>\n <\/div>\n <\/div>\n <\/div>\n <\/div>\n<\/div>\n\n\n\n
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Features:<\/h3>\n \n