creator Tong, Xin advisor Hickernell, Fred J. This thesis proposes a guaranteed, adaptive, automatic algorithm for solving univariate function minimization problem on the unit interval. The key to this adaptive algorithm is performing the analysis for cones of input functions that are twice differentiable. This cone is defined in terms of two semi-norms, a stronger one and a weaker one. Three fixed-cost algorithms based on linear splines are used to find the bounds for an input function and its minimum value. The estimated minimum value and possible optimal solution set are given by those bounds. This algorithm is guaranteed to provide either a minimum value within a user-specified tolerance or a possible optimal solution set whose volume is less than another user-specified tolerance. Submitted by Liana Khananashvili (khananashvili@iit.edu) on 2014-12-18T19:13:59Z No. of bitstreams: 2 A GUARANTEED, ADAPTIVE, AUTOMATIC ALGORITHM FOR UNIVARIATE FUNCTION MINIMIZAION by XinTong A20282371 M.S. in Applied Math.pdf: 201258 bytes, checksum: 5516362ec1b3622f37ebdcc3b5866745 (MD5) signed title page.pdf: 108971 bytes, checksum: ced1ee4461f442e758c4d78856a9ee54 (MD5) Made available in DSpace on 2014-12-18T19:13:59Z (GMT). No. of bitstreams: 2 A GUARANTEED, ADAPTIVE, AUTOMATIC ALGORITHM FOR UNIVARIATE FUNCTION MINIMIZAION by XinTong A20282371 M.S. in Applied Math.pdf: 201258 bytes, checksum: 5516362ec1b3622f37ebdcc3b5866745 (MD5) signed title page.pdf: 108971 bytes, checksum: ced1ee4461f442e758c4d78856a9ee54 (MD5) Previous issue date: 2014-07 M.S. in Applied Mathematics, July 2014 2014 2014-07 http://hdl.handle.net/10560/3371 en Thesis born digital application/pdf In Copyright http://rightsstatements.org/page/InC/1.0/ Restricted Access MATH / Applied Mathematics Illinois Institute of Technology Affiliated department